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New Pattern Mock Test - 2 - GRE MCQ


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30 Questions MCQ Test GRE Mock Test Series 2024 - New Pattern Mock Test - 2

New Pattern Mock Test - 2 for GRE 2024 is part of GRE Mock Test Series 2024 preparation. The New Pattern Mock Test - 2 questions and answers have been prepared according to the GRE exam syllabus.The New Pattern Mock Test - 2 MCQs are made for GRE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for New Pattern Mock Test - 2 below.
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New Pattern Mock Test - 2 - Question 1

Directions: For each sentence, choose one word for each set of blanks. Select the word or words that best fit(s) the meaning of the sentence as a whole.

Q. While most of the crowd was elated at the ______ promises that the politicians made, more cynical observers remained skeptical.

Detailed Solution for New Pattern Mock Test - 2 - Question 1

The key to this question is the contrast between the “elated,” or excited, crowd, and the “skeptical,” or doubting, cynics. We are looking for a word that would cause the crowd to be excited, but would cast doubt among skeptics. We can immediately eliminate choice (A) stolid, “unemotional,” choice (B) verbose, “talkative,” and choice (E) diffident, “lacking self-confidence,” as these are all negative adjectives for a political speech and would not invoke the excitement of the crowd.Choice (C) whimsical, “fanciful,” seems plausible: the crowd might like a fanciful, idealistic promise, while cynics would remain doubtful of its veracity.
However, choice (D) extravagant is a better choice, as it implies an attractive promise that might not be realistic.

New Pattern Mock Test - 2 - Question 2

One element, which may not justify violence itself but which __________ its use, is the belief that death in a sacred cause is the proper end of life.

Detailed Solution for New Pattern Mock Test - 2 - Question 2

Let us try to understand the meaning of the sentence from the partial information.

The sentence talks about an element that doesn't justify violence itself but does something to its use. This element is the belief that death, if for a sacred cause, can be considered a proper end of life. The structure and reasoning of the sentence implies that the element is trying to justify the use of violence. In other words, justify can be a good fill-in for the sentence.

Now, let us look at the meaning of the verbs in the options.

A. incriminates – to make (someone) appear guilty of a crime or wrongdoing
B. valorizes – to give or ascribe value or validity to
C. indicts – to formally accuse of or charge with a crime
D. abrogates – to abolish by authoritative action
E. rescinds – to take away
'Valorizes,' which means to give validity to something, is the correct answer. 'Incriminates,' 'indicts,' and 'abrogates' are opposite to what the context requires. 'Rescinds' does not go with the intended meaning of the sentence.

The correct answer is B.

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New Pattern Mock Test - 2 - Question 3

Directions: For each sentence, choose one word for each set of blanks. Select the word or words that best fit(s) the meaning of the sentence as a whole.

Q. The (i) _______ relationship between patients and their doctors is evidenced by patients’ (ii) _____ reactions to the attempts by insurance companies to force patients to see new doctors in different health care networks.

Detailed Solution for New Pattern Mock Test - 2 - Question 3

The first blank describes the “relationship” of patients with their doctors, and the second blank describes these patients’ “reactions” to Insurance companies. 
so, correct sentence be like: The (i) Laconic relationship between patients and their doctors is evidenced by patients’ (ii) Antagonistic reactions to the attempts by insurance companies to force patients to see new doctors in different health care networks.

New Pattern Mock Test - 2 - Question 4

Directions: For each sentence, choose one word for each set of blanks. Select the word or words that best fit(s) the meaning of the sentence as a whole.

Q. While the university’s adoption of a new policy against plagiarism was intended to (i) _____ the school’s faculty, some instructors criticized the policy as a (ii) _____ attempt to address a serious problem.

Detailed Solution for New Pattern Mock Test - 2 - Question 4

“While” is a detour road sign, indicating the contrast between what the university intended with the adoption of a new policy and the criticism that the policy received. For the first blank, predict that the policy was intended to satisfy or win the approval of the faculty. (B) is correct because mollify means to “appease” or “to make something better”; thus, mollifying the faculty would satisfy the faculty. (A), obviate, means to “prevent” or “eliminate,” which does not match the prediction.
Censure, (C), means “to show disapproval” or “to officially reprimand.”
For the second blank, you want a word that indicates how the faculty characterized the university’s attempt to address a "serious problem." Since the faculty was critical, predict that they thought the university’s policy was a poor or feeble attempt. (D) is correct because tepid means “lacking in force” or “unenthusiastic.” Pugnacious, (E), means “combative” or “inclined to fight.” Polarizing, (F), means “to divide into sharply opposing groups.”

New Pattern Mock Test - 2 - Question 5

Directions: For each sentence, choose one word for each set of blanks. Select the word or words that best fit(s) the meaning of the sentence as a whole.

Q. It was apparent that the recordings were ________ remastered, as the vocals were barely audible through the wave of noise.

Detailed Solution for New Pattern Mock Test - 2 - Question 5

The word “as” signals a continuation of ideas—the vocals were hard to hear because of the way the recordings were mastered. The answer is (A) maladroitly, which means “unskillfully” or “bunglingly.” Choices (B) copiously, (C) ingeniously, and (D) shrewdly are not in line with what you’re looking for—these words suggest more time and care than was spent. Choice (E) maliciously is too harsh. It’s doubtful the recordings were mastered with intent to harm.

New Pattern Mock Test - 2 - Question 6

Directions: For each sentence, choose one word for each set of blanks. Select the word or words that best fit(s) the meaning of the sentence as a whole.

Q. While the guitar has (i) _____ over the course of its centuries-long history, perhaps most notably with the invention of the electric guitar in the 1930s, the modern guitar exhibits (ii) _____ the vihuela of 15th-century Spain. A skilled guitarist would likely be able to pick up this (iii) _____ instrument, also an ancestor of the viol, andcompetently play a tune.

Detailed Solution for New Pattern Mock Test - 2 - Question 6

The first blank is a good one to start with here. It describes something that’s happened to the guitar over its long history. Since the given example is the invention of the electric guitar, you can predict that the guitar has “grown” or “changed.” (B) evolved is a match and is correct. (A) stagnated, or “remained the same,” doesn’t fit, as an innovation is specifically mentioned in the first sentence. (C) regressed, or “moved backward,” does imply a change, but there’s no indication that the guitar has changed in a negative or regressive fashion.

The second blank explains the relationship between a modern guitar and a 15th-century instrument. “While” is a detour road sign; it indicates that there’s a contrast between this relationship and the evolution of the guitar. Furthermore, the second sentence indicates that a skilled guitarist would be able to “competently” play the vihuela. A good prediction would be that even though the guitar has gone through changes over the centuries, it is still similar to the vihuela. This idea is reinforced by the next sentence, which says that a modern guitarist could probably play the old instrument. (E) an affinity to is the correct answer; an affinity is a “similarity” or a “likeness.” (D) an incongruity with and (F) a divergence from both indicate a dissimilarity with the vihuela, which is not supported.

The third blank is directly connected to the vihuela; since all that’s known about it from this text is that it’s from the 15th century, predict that this blank means “old.” That’s (H) archaic, which means “outmoded” or “antiquated.” (G) inferior (“of lesser quality”) is wrong because there’s no support for the idea that the vihuela is worse than the guitar or any other instrument. (I) avant-garde may be tempting because it’s a term that’s oen used in the context of music and other arts; however, it relates to “new” or “experimental” concepts, so it doesn’t fit here.

New Pattern Mock Test - 2 - Question 7

Directions: For each sentence, choose one word for each set of blanks. Select the word or words that best fit(s) the meaning of the sentence as a whole.

Q. The punctilious wine aficionado was a consummate purist when it came to his tastes. He immediately rejected the (i) _______ of two wines. As an alternative, and as a generalrule, he preferred a simple, (ii) ______ wine.

Detailed Solution for New Pattern Mock Test - 2 - Question 7

The key to this sentence is the description of the wine aficionado (or expert) as a “purist,” or someone who insists on the purity of things.
Since he rejects the first blank, you can assume it will be an antonym of pure. You can predict mixture, which fits in the context. However, he prefers the second blank, so this should be a synonym of pure and the contextual word “simple.”
For the first blank, the best match for your prediction is choice (A) amalgamation. This is an exact synonym of your prediction, mixture.
Choice (B) dissonance, which means “a disagreeable combination,” seems plausible. A purist would definitely find a mixture of two wines to be dissonant. However, we need a word that states this mixture has occurred for the sentence to make sense. Similarly, choice (C) enigma means “puzzle,” which may also be applicable to such a mixture but, again, lacks the necessary meaning of “mixture.” For the second blank, choice (E) unadulterated matches your prediction best. Choice (D) pragmatic means “practical” and does not fit as well as unadulterated in context. The wine aficionado does not prefer something for its practicality but for the taste; therefore, this choice would be misleading in the sentence. Choice (F) opaque, which means “impossible to see through,” may similarly be applicable to the wine; however, nowhere in the sentence is the color implied or relevant.

New Pattern Mock Test - 2 - Question 8

Directions: Read the following passage and answer the question.
All artists are reputed to suffer to some degree for their art, but some may physically suffer more than others. As part of The 3rd I project, a performance artist agreed to have a camera surgically implanted into the back of his head and the footage gathered from the experiment to be uploaded hourly into a website. The surgery involves slicing and lifting folds of skin and implanting the camera into the back of the skull and is excruciating for the artist. Some critics claim that the visceral reaction of hearing about the camera or its insertion may be orchestrated to shock viewers into learning more about the art or the project. Although the camera can be fitted with a lens cap to protect the privacy of those who request it, every single detail of the artist’s life is recorded and open for all to view. One might conclude that this project is an extreme example of the Modernists’ tendency to take the creation of art as its subject.

Q. The passage implies that the strength of the reaction the artwork evokes would be substantially weakened if which of the following were to happen?

Detailed Solution for New Pattern Mock Test - 2 - Question 8

This Inference question asks you to identify statements about people's reaction to the artwork that follow from the passage. According to the critics mentioned in the passage, knowing how the art was created is potentially related to the audience’s interest in it. The reaction is mainly reliant on the concept, not the product, of the art. Thus, (B) is correct; if the audience doesn’t appreciate how the art was made, they may be less interested in it. Choice (A) doesn’t follow from the passage. Nothing suggests that the beauty or clarity of the images produced affects the success of the project. If (C) were true, it would likely increase the popularity of the performance and get people thinking about it. This has the opposite effect called for by the question stem.

New Pattern Mock Test - 2 - Question 9

xy > 0
Quantity A
x2y4 
Quantity B
x3y6

Detailed Solution for New Pattern Mock Test - 2 - Question 9

Given: xy > 0.
⇒ xy is a positive quantity.
There can be two cases here.
Case 1: Both x and y are positive
Let's analyze the values of Quantity A (x2y4) and Quantity B (x3y6).
Case 1.1: Say x = y = 1
Quantity A: x2y= 12 × 14 = 1
Quantity B: x3y6 = 13 × 16 = 1
We see that Quantity A equals Quantity B.
Case 1.2: Say x = y = 2
Quantity A: x2y= 22 × 24 = 26
Quantity B: x3y6 = 23 × 26 = 29
We see that Quantity B is greater than Quantity A. No unique answer from the two cases discussed so far, thus the correct answer is option D.
Though we concluded that the correct answer is option D, we can analyze Case 1.3 and Case 2 also for the sake of understanding.

We see that Quantity A is greater than Quantity B.
Thus, there are all the possible answers A, B and C possible when we consider that both x and y are positive.
Let's discuss the case when both x and y are negative.
Case 2: Both x and y are negative
Quantity A: x2y4
Since the exponents of x and y are even, the value of x2 & y4 would be positive irrespective of whether their values are negative. So, x2y= ∣∣x2∣∣ × ∣∣y4∣∣ = a positive number>0.
Quantity B: x3y6
Since the exponent of x is odd, and x is negative, the value of x3 would be negative. As discussed above that since the exponents of y is even, the value y6 would be positive irrespective of whether its value is negative.
So, x3y= −∣∣x3∣∣ × ∣∣y6∣∣ = a negative number < 0.
Thus, quantity A is greater than B for Case 2.

New Pattern Mock Test - 2 - Question 10

In the figure shown below, line segment BC has length 16 cm, rectangle FABE is a square, and the area of rectangular region FACD is 612 cm2.

Quantity A
Area of FABE
Quantity B
Area of EBCD

Detailed Solution for New Pattern Mock Test - 2 - Question 10

Given:

  • BC = 16 cm
  • Rectangle FABE is a square
  • The area of rectangular region FACD = 612 cm2

We have to compare the Area FABE and Area EBCD.
Say the side of the square FABE is xcm. Thus, AF = x and AC = AB + BS = x + 16
Thus, Area of FACD = x ×(x + 16) = 612 (given)
So, we have x(x + 16) = 612
⇒ x2 + 16x − 612 = 0
x2 + 34x − 18x − 612 = 0
x(x + 34) − 18(x + 34) = 0
(x + 34)(x − 18) = 0
⇒ x = 18 since x = −34 (not possible; side cannot be negative)
Quantity A: Area FABE = FA × AB = x × x = x2 = 182 cm2
Quantity B: Area EBCD = EB × BC = x × 16 = 18 × 16cm2
It is clear that Quantity A (= 182) is greater than Quantity B (18 × 16).

New Pattern Mock Test - 2 - Question 11

Working independently, Machine A can complete a work in 3.5 hours, while Machine B can complete the same work in x hours. Working simultaneously, they together complete the same work in 1.5 hours.

Quantity A
3
Quantity B
x

Detailed Solution for New Pattern Mock Test - 2 - Question 11

Given:

  • Machine A working ALONE can complete a work in 3.5 hours
  • Machine B working ALONE can complete the same work in x hours
  • Machine A & B working together can complete the same work in 1.5 hours

We have to find the value of x and compare it with 3.
The part of work Machine A working ALONE completes in one hour = 1/.35 = 2/7
The part of work Machine B working ALONE completes in one hour = 1/x
Thus, the part of work Machine A & B working together completes in one hour 


x = 2.625 hours.
Thus, Quantity A (=3) is greater than Quantity B (= x = 2.625).

New Pattern Mock Test - 2 - Question 12

A driver completed the first 20 miles of a 40-mile trip at an average speed of 50 miles per hour and the second 20 miles at an average speed of x miles per hour. The average speed for the entire 40-mile trip was 60 miles per hour. (Assume that the driver did not make any stops during the 40-mile trip.)
Quantity A
x − 60
Quantity B
10

Detailed Solution for New Pattern Mock Test - 2 - Question 12

Given:

  • Average speed for the first 20 miles of a 40-mile trip =50miles per hour
  • Average speed for the second 20 miles of a 40-mile trip =xmiles per hour
  • Average speed for the entire 40-mile trip =60miles per hour

We have to find the value of x and compare it with (x−60).
Time taken to complete first 20 miles of a 40-mile trip 

Time taken to complete second 20 miles of a 40-mile trip

Time taken to complete the entire 40-mile trip


We have, Quantity A = x − 60 = 75 − 60 = 15
Thus, Quantity A (=15) is greater than Quantity B (=10).

*Answer can only contain numeric values
New Pattern Mock Test - 2 - Question 13

At a certain store for a certain month, in a chart given below, the price per cell phone (in dollars) is shown by dots (read from right hand side vertical axis) and the number of cell phones sold (read from left hand side vertical axis).

gre-neq-1-1

Q. What is the median price of the cell phones sold by the store in that month?


Detailed Solution for New Pattern Mock Test - 2 - Question 13

To determine the median price, we first need to arrange the items per ascending or descending order of their price. We chose to do it in ascending order. Thus, we have the following table:

Since the total number of cell phones sold is 450, the median value

= Price of the item/cell phone

= Price of the(225.5)th item/cell phone

= Average of the price of the 225th item and the price of the226th item

We see that the 225th item lies in 225th cumulative number of units' column in the table, thus, its price would be the price of the brand that lies in the same row of the 225th cumulative item. We find that it is $250.

Similarly, we see that the 226th item lies in 300th cumulative number of units' column in the table, thus, its price would be the price of the brand that lies in the same row of the 300th cumulative item. We find that it is $350.

Thus, the median price per cell phone = 

Note that the median price per phone (= $250) would not be the price of the middle-most brand if the prices are arranged in ascending order: 150, 200, 250, 350, and 400. This is because the logic is flawed. In this case the number of units per brand of cell phone sold is ignored.

*Answer can only contain numeric values
New Pattern Mock Test - 2 - Question 14

At a certain store for a certain month, in a chart given below, the price per cell phone (in dollars) is shown by dots (read from right hand side vertical axis) and the number of cell phones sold (read from left hand side vertical axis).

gre-neq-1-1

Q. What is the mean price (nearest to a dollar) of the cell phone sold by the store in that month?


Detailed Solution for New Pattern Mock Test - 2 - Question 14

To determine the mean price, we need to find the Total sales. Thus, we have the following table:

Mean price per item/cell phone  = Total sales / Total number of units sold = 128750 / 450

= $286.11
= ∼$286

*Answer can only contain numeric values
New Pattern Mock Test - 2 - Question 15

If x is an integer, how many possible values of x satisfy the equation: (x−2)2(x+1) = 1


Detailed Solution for New Pattern Mock Test - 2 - Question 15

Possible solutions of ab = 1 are as follows:

  • a = 1; for any value of b
  • a = −1 and b is even
  • b=  0; for any value of a other than a = 0
  • From a): a = x − 2 = 1 ⇒ x = 3: one of the possible values of x
  • From b): a=  x − 2 = −1 ⇒x = 1; we see that b = 2(x + 1) = 2(1 + 1) = 4 is an even integer, thus x = 1 is one of the possible values of x
  • From c): b = 2(x + 1) = 0 ⇒ x = −1; at x = −1, we see that a = x − 2 = −1 − 2 = −3 ≠ 0; thus, x = −1 is one of the possible values of x

There are three possible values of x: -1, 1, and 3.

Let's cross-check these values for the sake of better understanding.

  • At x = −1, we have (x − 2)2(x + 1) = (−1 − 2)2(−1 + 1) = −30 = 1 = RHS
  • At x = 1, we have (x − 2)2(x + 1) = (1 − 2)2(1 + 1) = −14 = 1 = RHS
  • At x = 3, we have (x − 2)2(x + 1) = (3 − 2)2(3 + 1) = 18 = 1 = RHS
New Pattern Mock Test - 2 - Question 16

If ABC is a straight line as shown in the figure below, and the angles x & y are integer multiples of 20, what is the value of x?

Detailed Solution for New Pattern Mock Test - 2 - Question 16

Given:

  • ABC is a straight line
  • Angles x & y are integer multiples of 20

We have to find out the value of x.
We have:
2x + 3y = 180
Let x = 20p and y = 20q, where p and q are positive integers
⇒ 40p + 60q = 180
⇒ 2p + 3q = 9
The only possible ordered pair of positive integers for p & q are {3,1}.
Thus, x = 20p = 20 × 3 = 60°.

New Pattern Mock Test - 2 - Question 17

 what is the value of x2?

Detailed Solution for New Pattern Mock Test - 2 - Question 17

Given:

We have to find out the value of x2.
Let's first solve this with the traditional method and then we would solve it through alternate approaches.
We have 
Squaring both the sides, we get:

Again, squaring both the sides, we get:
4(x + 6)(x + 1) = (18 − 2x)2 
4x+ 28x + 24 = 324 − 72x + 4x2
100x = 300
x = 3 ⇒ x2 = 9

*Answer can only contain numeric values
New Pattern Mock Test - 2 - Question 18

Suzy purchased at least one pen priced at $13 each and at least one notebook priced at $19 each. If the total price of the items purchased is $58, what is the total number of pens and notebooks purchased by Suzy?


Detailed Solution for New Pattern Mock Test - 2 - Question 18

Let the number of pens and notebooks purchased be x and y, respectively.

⇒ 13x + 19y = 58
The number of pens and notebooks purchased must be positive integers.

Let us try with a few positive integer values of x and calculate the qualified values of y:

x = 1: 13 + 19y = 58 ⇒ y = 45/19 = not an integer - Not a valid solution

x = 2: 26 + 19y = 58 ⇒ y = 32/19 = not an integer - Not a valid solution

x = 3: 39 + 19y = 58 ⇒ y = 1 - A valid solution

Thus, for all other higher values of x, the value of y would be either less than 1 or negative and hence can be ignored.

Total number of items purchased by Suzy  = x + y = 3 + 1 = 4

*Multiple options can be correct
New Pattern Mock Test - 2 - Question 19

What could be the values of integers from 180 to 300, inclusive, that leave the remainder 2 when divided by 15 and by 9?

Indicate all such numbers.

[ Note: Select one or more answer choices ]

Detailed Solution for New Pattern Mock Test - 2 - Question 19

Since the number leaves a remainder 2 when divided by 15 and by 9, the number would leave the same remainder '2' when divided by the Least common multiple (LCM) of 15 and 9, i.e. 45.

We need to find the numbers between 180 and 300, inclusive, that leave the remainder 2 that are in the format (45n + 2); where n is a positive integer.

We know that 180 ≤ 45n + 2 ≤ 300
180 − 2 ≤ 45n ≤ 300 − 2
= 178 ≤ 45n ≤ 298
= 17845 ≤ n ≤ 29845
= 3.96 ≤ n ≤ 6.62
= n = 4,5,or 6
Thus, the required numbers are:

45n + 2 = 45 × 4 + 2 = 182
45n + 2 = 45 × 5 + 2 = 227
45n + 2 = 45 × 6 + 2 = 272

New Pattern Mock Test - 2 - Question 20

The sequence a1,a2,a3,…an,… is such that a1 = −2, a2 = −5, a3 = 4, a4 = 3, and an = an−4 for n >4.
Quantity A
The sum of the first 64 terms of the sequence
Quantity B
The sum of the first 98 terms of the sequence

Detailed Solution for New Pattern Mock Test - 2 - Question 20

Given:
a1 = −2, a2 = −5, a3 = 4, a4 = 3,and an = an−4 forn > 4
We have to compare the sum of the first 64 terms and the first 98 terms of the sequence.
Since the question involves the sum of the terms up to 98 terms, which is a big number, you must anticipate that there is some kind of pattern in the sequence.
We have the values for the first 4 terms: a1 = −2, a2 = −5, a3 = 4,and a4 = 3.
It is given that for n > 4, an = an−4
Thus,

  • a5 = a5 − 4 = a1 = −2
  • a6 = a6 − 4 = a2 = −5
  • a7 = a7 − 4 = a3 = 4
  • a8 = a8 − 4 = a4 = 3

You would observe that there is a pattern of 4 terms in the sequence. 5th term onwards of the sequence repeats.
Thus, Quantity A: the sum of the first 64 terms of the sequence
= (a1 + a2 + a3 + a4)+(a5 + a6 + a7 + a8)+...+(a61 + a62 + a63 + a64)
= (−2−5 + 4 + 3) + (−2−5 + 4 + 3)+...+(−2−5 + 4 + 3)
 there would be 64/4 = 16 groups with each having their value equal to 0.

Similarly, Quantity B: the sum of the first 98 terms of the sequence
= (a1 + a2 + a3 + a4) + (a5 + a6 + a7 + a8)+...+(a93 + a94 + a95 + a96)+(a97 + a98
=(−2−5 + 4 + 3)+(−2−5 + 4 + 3)+...+(−2−5 + 4 + 3)+(−2−5)

We see that Quantity A (= 0) is greater than Quantity B (= −7).

New Pattern Mock Test - 2 - Question 21

3, a, 1, 9, b, 3
The arithmetic mean of the list of numbers above is 4 and a and b are integers.
Quantity A
Median of the list
Quantity B
Mean of the list

Detailed Solution for New Pattern Mock Test - 2 - Question 21

Given:

  • The arithmetic mean of the list {3, a, 1, 9, b, 3} = 4
  • a and b are integers

We have to compare the Median and the Mean (= 4) of the list.
Let's first find out the relationship between a and b by using the information that the arithmetic mean of the list {3, a, 1, 9, b,3 } = 4

⇒ a + b = 24 − 16 ⇒ a + b = 8
We already know Quantity B (= Mean = 4); we need to calculate the value of Median.
So, we have a+b=8. Let's discus two extreme cases.
Case 1: Say a = −2. Thus, b = 8 − (−2) = 10
So, the list arranged in an ascending order is {−2,1,3,3,9,10}.

We see that Quantity A (= 3) is less than Quantity B (= 4).
Case 2: Say a = b = 4.
So, the list arranged in an ascending order is {1,3,3,4,4,9}.

We see that Quantity A (= 3.5) is less than Quantity B (= 4).
There is no need to consider the case which has b=−2 & a=10 since that would be the same as Case 1.
We cannot consider a case which has a=3.5 because that would be an invalid case since a & b both are integers.
Thus, median of the list would be either 3 or 3.5, and in either case, Quantity A (= 3 or 3.5) is less than Quantity B (= 4).

New Pattern Mock Test - 2 - Question 22


Quantity A
Maximum value of −(5 − x)
Quantity B
Maximum value of 2x

Detailed Solution for New Pattern Mock Test - 2 - Question 22

Given:

We have to compare the maximum value of −(5−x) and the maximum value of 2x.
Let's first find out the range of x.
We have 

⇒ 12 < 7 − x ; multiplying both the sides by +3; we can multiply/divide the inequality by a positive number without changing the sign of the inequality and can do so by a negative number but with reversing the sign of the inequality
= 5 < −x; subtracting both the side by 7
= − 5 > x; reversing the sign of inequality
We see that x is a negative number and can have any large negative value.
Quantity A: Maximum value of −(5 − x)
⇒ Maximum value of (x − 5)
Since x is negative, and we need to get the maximum value of (x−5), the least possible value of x in the magnitude would be eligible
Say x = −5.001
Maximum value of (x − 5) = −5.001 − 5 = −10.001
Quantity B: Maximum value of 2x at x = −5.001
Maximum value of 2x = 2 × −5.001 = −10.002
Thus, Quantity A (=-10.001) is greater than Quantity B (=-10.002).
No matter how close to -5, you choose the value of x, you would find that Quantity A is greater than Quantity B. Let's take another example.
Say x=−5.00001
Maximum value of (x − 5) = −5.00001 − 5 = −10.00001
Quantity B: Maximum value of 2x at x = −5.00001
Maximum value of 2x = 2 × −5.00001 = −10.00002
Thus, Quantity A (=-10.00001) is greater than Quantity B (=-10.00002).

*Answer can only contain numeric values
New Pattern Mock Test - 2 - Question 23

The following chart shows the percent distribution of the number of candidates enrolled in a certain test-prep company from 2014 to 2017 for four courses: GMAT, GRE, SAT and LSAT.

gre-neq-3-1

Q. If the total number of candidates increased by 40% from the year 2014 to the year 2017, what is the simple annual percent increase (if necessary whole number rounded) in the number of candidates for the GMAT course between 2014 and 2017?


Detailed Solution for New Pattern Mock Test - 2 - Question 23

Let the number of candidates in the year 2014 be 100.

Thus, the number of candidates in the year 2017 = 100 + (100 × 40%) = 140
Number of candidates for the GMAT course in 2014 = 35% of 100 = 35; read data from the chart

Number of candidates for the GMAT course in 2017 = 45% of 140 = 63; read data from the chart

Thus, percent increase = 
This increase happened over a period of 3 years: 2014-2015, 2015-2016 and 2016-2017.

Thus, the simple annual percent increase = 80 / 3 = 26.67% ⇒ 27% as whole number rounded

The answer is not 80% since the question asked to calculate the simple annual percent increase for three years.

*Answer can only contain numeric values
New Pattern Mock Test - 2 - Question 24

The following chart shows the percent distribution of the number of candidates enrolled in a certain test-prep company from 2014 to 2017 for four courses: GMAT, GRE, SAT and LSAT.

gre-neq-3-1

Q. If the number of candidates in 2014 was 500, and there was a 20% increase in the number of candidates per year for the next two years, what is the number of candidates for the LSAT course in 2016?


Detailed Solution for New Pattern Mock Test - 2 - Question 24

We know that the total number of candidates in 2014 was 500.

Since every year for the next two years, i.e., for 2014-2015 and 2015-2016, the percent increase in the number of candidates is 20%, the number of candidates in 2015 = 120% of 500 = 600.

Similarly, number of candidates in 2016 = 120% of 600 = 720.

Thus, the number of candidates for the LSAT course in 2016 = 15% of 720 = 108; from the 2016 chart, we know that there are 15% candidates for the LSAT course.

Alternatively, you can calculate it as following:

C2016 = C2014 × (1+r%)n; say C2016 = number of candidates in 2016, C2014 = number of candidates in 2014, the rate of increase = r% and the number of years = n
C2016 = 500 × (1 + 20%)2; given that C2014 = 500, r% = 20%, and there are 2 years from 2014 to 2016, thus n = 2
C2016 = 500 × 1.22 = 500 × 1.44 = 720
Thus, the number of candidates for the LSAT course in 2016 = 15% of 720 = 108.

*Answer can only contain numeric values
New Pattern Mock Test - 2 - Question 25

n the figure below, a square ABCD is inscribed in a circle. If the length of arc AB is 4π unit, what is the diameter of the circle?

gre-neq-6-1


Detailed Solution for New Pattern Mock Test - 2 - Question 25

Let O be the center of the circle and the square and rr be the radius of the circle.

gre-neq-6-2

Since the diagonals of a square are perpendicular, ∠AOB = 90°

Length of an arc subtending angle θ° at the center of the circle = 2πr × (θ / 360)

Thus, length of the minor arc AB = 2πr × (90 / 360) = πr / 2; since θ° = 90°

Thus, we have: πr / 2 = 4π

⇒ r = 8unit

⇒ Diameter = 2r = 16unit

*Multiple options can be correct
New Pattern Mock Test - 2 - Question 26

In a certain batch of guests in a museum, there are 50 guests; each guest buys either a $40 ticket or a $60 ticket, with at least one guest of each ticket type. The average (arithmetic mean) value of ticket-receipts from the batch is more than $50. If the average value of ticket-receipts is to be reduced to less than $50 by including few new guests with $40 tickets, what could definitely NOT be the number of new guests with $40 tickets that could be included?

Indicate all such numbers.

[ Note: Select one or more answer choices ]

Detailed Solution for New Pattern Mock Test - 2 - Question 26

We have 50 guests and each has either a $40 ticket or a $60 ticket with an average ticket-receipt of more than $50. We need to include few new guests with $40 tickets so that the average ticket-receipt of all the guests becomes less than $50.

We see that if the number of guests with $40 tickets and the number of guests with $50 tickets initially were equal in number, i.e. 50/2 = 25 each, the average ticket-receipt of all the guests would be

= $50  (i.e. the simple average of $40 and $60)

Since it is given that the average ticket-receipt is more than $50, we can conclude that the number of guests with $60 tickets is greater than the number of guests with $40 tickets.

Thus, currently, there are 26 or greater guests with $60 tickets and 24 or fewer guests with $40 tickets.

Since we finally need to reduce the average ticket-receipt of all the guests to less than $50, we must have a greater number of guests with $40 ticket than the number of guests with $60 ticket.

This means that the guests with $40 tickets must be greater than 26 or at least 27. Presently, there are 24 guests with $40 tickets; thus, 3 or more new guests with $40 tickets must be included to reduce the average ticket-receipt of all the guests to less than $50.

Thus, we can see that if including either 1 or 2 number of guests with $40 tickets would definitely not be sufficient.

New Pattern Mock Test - 2 - Question 27

If two interior angles of a quadrilateral ABCD are right angles and the degree measure of ∠ABC is twice the degree measure of ∠BCD, what could be the measure of the largest interior angle of quadrilateral ABCD?

Indicate all such angles.

Detailed Solution for New Pattern Mock Test - 2 - Question 27

We know that two of the interior angles are 90° each.

Since the sum of the angles of a quadrilateral is 360°, the sum of the other two angles

=360° − (90° + 90°) = 180°

We know that:

∠ABC = 2 × ∠BCD

Let us consider all possible cases for the relation ∠ABC = 2 × ∠BCD

  • Say ∠BCD = 90° ⇒ ∠ABC=2 × ∠BCD = 180°

    Since one more angle is 90°, the measure of the fourth angle

    = 360° − (90° + 90° + 180°) = 0° - This is not possible since this will not render a quadrilateral.

  • Say ∠ABC = 90° ⇒ ∠BCD = 90°/2 = 45°

    Since one more angle is 90°, the measure of the fourth angle

    =360°− (90° + 90° + 45°) = 135° 

    Thus, the largest interior angle among 90°, 90°, 45°, and 135° is 135° -Option D is correct

  • Neither ∠ABC∠ABC nor ∠BCD∠BCD is equal to 90°

    Thus, we have:

    ∠ABC + ∠BCD = 360° − (90° + 90°) = 180°

    Since one angle between ∠ABC and ∠BCD is twice the other, we have:

    Smaller angle = (1 /1 + 2) × 180° = 60°

    Larger angle = 180° − 60°=120°

    Thus, the largest interior angle among 90°, 90°, 60°, and 120° is 120° - Option C is correct

*Answer can only contain numeric values
New Pattern Mock Test - 2 - Question 28

If a group of students having an average age of 16 years joined a class, the average age of all the students in the class reduces from 18 years to 17 years. What is the ratio of the number of students who joined the class to the number of students who were initially in the class?


Detailed Solution for New Pattern Mock Test - 2 - Question 28

Let the number of students in the class before the group of students joined = x
Let the number of students who joined the class = y
It is given that the initial average age of the class = 18years
The average age of the group of students who joined the class = 16years
The average age of all the students after the group of students joined  = 17years
Thus, we have:

⇒ 18x + 16y = 17x + 17y

⇒ y / x = 1

*Answer can only contain numeric values
New Pattern Mock Test - 2 - Question 29

A 120-milliliter mixture of Chemical X and water contained 40 percent Chemical X. A part of the mixture was removed and replaced with an equal quantity of water. If the resulting mixture contained 10 percent Chemical X, what is the volume of the mixture that was removed?


Detailed Solution for New Pattern Mock Test - 2 - Question 29

Volume of the original mixture = 120ml
Volume of Chemical X present = 40% of 120ml = 48ml
Let x ml of the mixture be removed.

Percent of Chemical X present in x ml is also 40%
Thus, the volume of Chemical X removed = 40% of x ml = 2 / 5x ml
Thus, volume of Chemical X remaining =

Total volume of the mixture left = (120 − x)ml
Volume of water added = x ml
Thus, total volume of the final mixture

= (120 − x) + x = 120ml
Final volume of Chemical X = 10% of 120 = 12ml
Thus, from (i), we have:

48 − 2 / 5x = 12
⇒ x = 90ml

New Pattern Mock Test - 2 - Question 30

If x and y are non-negative integers such that 2x + 3y = 8 and z = x2 + y2, what is the maximum value of z?

Detailed Solution for New Pattern Mock Test - 2 - Question 30

Given:
x and y are non-negative integers such that 2x + 3y = 8 and z = x2 + y2.
We have to find out the maximum value of z.
We have 2x + 3y = 8

Since x and yx are positive integers, (4 − x) must be a multiple of 3. Only two eligible values of x are possible, and they are 1 and 4.
The set of values of x & y are {1,2} and {4,0}.

  • Value of z = x+ y2 at {1, 2}: z = x+ y2 = 1+ 2= 1 + 4 = 5
  • Value of z = x+ y2 at {4, 0}: z = x+ y= 4+ 02 = 16 + 0 = 16

The maximum of the two values 5 and 16 is 16 and that is the correct answer.

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