GMAT Focus Edition Mock test - 5 - GMAT MCQ

As we are trying to minimise the value of the expression |77 – 6p|, our aim should be to minimise the value of 77 – 6p.

• The value of 77 – 6p will be minimum, when 6p will be maximum
• The value of 6p will be maximum, when the value of p will be maximum

Now, we also know that p is a non-positive number.

• Therefore, the maximum value of p = 0

Hence, the correct answer is option D.

The correct response is (E). 5/7 = .7142…. Already there are more than four unique digits, which is more than any other number in the answer choices. Remember for each value there are only ten possible digits for each placeholder in a number: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The word “unique” means different from the other digits.

If you chose (A), 1/6 = .166666. There are only two unique digits in this number: 1 and 6.

If you chose (B), 1/4 = .25. There are only two unique digits in this number: 2 and 5.

If you chose (C), 1/3 = .333333. There is only 1 digit in this number: 3.

If you chose (D), 3/4 = .75. There are only two unique digits in this number: 7 and 5.

To make things a little easier on our brains, we can take the given inequality −145 < −|n²| < −120...
...and multiply all sides by -1 to get: 145 > |n²| > 120 [aside: Since we multiplied the inequality by a negative value, we reversed the direction of the inequality symbols]
So we're looking for squares of integers BETWEEN 120 and 145.
121 and 144 are the only squares of integers between 120 and 145
However, before we choose answer choice B, we must keep in mind that there are two values of n such that n² = 121 and there are two values of n such that n² = 144
If n² = 121, then n = 11 or n = −11
If n² = 144, then n = 12 or n = −12
So, there are FOUR possible values of n that satisfies the given conditions.

The correct response is (C). To solve algebraically, start by taking the square root of .00000256. We know the square root of 256 = 16. We can write 0.00000256 in scientific notation as 256 x 10^-8. So:

To double-check, you can backsolve:
04 x .04 = .0016, and .0016 x .0016 = .00000256.

If you chose (A), you miscalculated by one decimal point. Check your work by backsolving: .004 x .004 = .000016. And .000016 x .000016 = .000000000256 (four extra zeros).

If you chose (B), you need to take the square root twice. Zeros aside, the square root of 256 = 16, and the square root of 16 = 4.

If you chose (D), you miscalculated the zeros and you forgot to take the square root twice. If you backsolved to check your work you’d see that .16 x .16 = .0256. That result squared will not give us .00000256.

If you chose (E), you missed the correct choice by one decimal point. If you backsolved to check your work, you’d see that .4 x .4 = .16, and .16 x .16 = .0256, which is much larger than our original number from the question stem.

Rate of pump X = 1/8

3 hours are required to pump out the remaining (3/4)ths of tank → 1 hr to pump out 1/4

Rate of X + Rate of Y + Rate of Z = 1/4

Rate of Y + Rate of Z = 1/4 - 1/8 = 1/8

Y takes 18 hours to pump out the remaining (3/4)ths of tank → 6 hrs per (1/4)ths → 24 hrs to pump out fully.

Rate of Y = 1/24

1/24 + Rate of Z = 1/8

Rate of Z = 1/8 - 1/24 = 1/12

Time required to pump out all the water by Z = 12 hrs.

The correct response is (A). Let P be the number of Political Science majors and let R be the number of International Relations majors. "One fifth of the legislators are neither," so there are 1/5 *200 = 40 legislators who are neither. Hence, there are 200 – 40 = 160 Poly-Sci majors and IR majors, or P + R = 160. Translating the clause "the number of Poly-Sci majors is 50 less than 4 times the number of IR majors" into an equation yields P = 4R – 50.

Plugging this into the equation P + R = 160 yields:

4R – 50 + R = 160
5R – 50 = 160
5R = 210
R = 42

Here's a nice property of fractions: If a, b and k are positive, then (a + k)/(b + k) approaches 1 as k gets bigger.
For example, the fraction (2 + 11)/(3 + 11) is closer to 1 than 2/3 is.
Likewise, the fraction (1 + 7)/(2 + 7) is closer to 1 than 1/2 is.
Let A = Anna's present age
Let P = Paula's present age
So, A/P = 3/4
In EIGHT YEARS, we can conclude that:
Let A + 8= Anna's future age
Let P + 8 = Paula's future age
So, in EIGHT YEARS, the ratio of their ages = (A + 8)/(P + 8)
By the above rule, we know that (A + 8)/(P + 8) is closer to 1 than is A/P is.
In other words, (A + 8)/(P + 8) is closer to 1 than 3/4 is.
Check the answer choices.
Only answer choice E (aka 4/5) is closer to 1 than 3/4 is.

Assuming the rates of machines R, S, and T are r, s, and t, respectively, we are given:

• r + s + t = 1/4 and r = 1/6.

Subtracting the second equation from the first results in:

• s + t = 1 = 1/4 - 1/6 = 1/12.

Since rate is the reciprocal of time, machine S and machine T, would take 12 hours to produce the same batch of parts.

Given: From the even numbers between 1 and 9, two different numbers are chosen at random
To find: What is the probability that their sum will be 8
Approach and Working: Between 1 and 9, the even numbers are 2, 4, 6, and 8

• The only way sum of two different numbers among them is equal to 8 can be 2 + 6 or 6 + 2

The first number out of 2 and 6 can be selected in 1/2 ways

• Once the first number is chosen, we need to choose the 2nd number either from (2, 4, 8 – when the 1st chosen number is 6) or from (4, 6, 8 – when then 1st chosen number is 2).
• Therefore, this choice can be made in 1/3 ways

Hence, the required probability = 1/2 ∗ 1/3 = 1/6
Hence, the correct answer is option A.

The correct response is (C). The need-to-know formula here is: Profit/Loss % = (Sales Price – Cost Price) / Cost Price x 100. The stem tells us that 20c = 25s, or 4c = 5s, so the ratio of the sales price to the cost price is 4/5.
Let’s simplify our Profit/Loss % formula by dividing each term by the cost price: Profit/Loss % = (S/C – C/C) x 100
P/L% = (S/C – 1) x 100 We know that S/C = 4/5 for this problem. So we can plug in and solve:
P/L% = (4/5 – 1) x 100
P/L% = (-1/5) x 100
P/L% = -20%. The answer is a 20% loss.

Sales tax is 2% on the purchase price.
Another sales tax of 0.5% on the purchase price.
Therefore, total sales tax imposed on the purchase price = 2.5%
Let purchase price = p
2.5% of p = $2.80
On solving, p = $112.
The answer will be C.

Given:
s and t are positive integers
s/t = 39.12
To find: Find one of the possible value of t
Approach and Working out:
s = 39 t + 0.12 t
S and t are integer.
So, 0.12 t must also be an integer.
0.12 t = 12/100 t = 3/25t
For 3/25 t to be an integer, t must be divisible by 25.
Hence, option E is the correct answer.

water = w (liter)
Milk = m (liter)
=> Cost = Price x Quantity = 0.33m
=> Revenue = Price x Quantity = 0.36(m + w)
=> Profit = 0.36(m+w) - 0.33m = 0.2*(0.33m) [20% of cost]
=> 0.36m + 0.36w - 0.33m = 0.066m
=> 0.036m = 0.36w
=> m/w = 0.36/0.036 = 10
--OR--
w/m = 1/10
B is correct.

The correct response is (C). The denominator of any fraction is undefined when it equals 0, so x cannot be 4 in this expression. However, the question asks what cannot be a value for 1 / 4 – x. 1 divided by any number cannot equal zero.
If you chose (A), it is possible for 1 / 4 – x = -4 if x = 17/4.
If you chose (B), it is possible for 1 / 4 – x = 4/17 if x = -1/4.
If you chose (D), remember the question is asking what the expression can equal, not the possible values for x. This is a “trap” answer choice!
If you chose (E), it’s possible for 1 / 4 – x = 17/4 if x = 64/17.

Using the formula given for numbers 3 and above we get,

This sequence is neither an Arithmetic Progression nor a Geometric Progression. So, let's try Harmonic Progression by taking reciprocal of all numbers.
Now we get 
Clearly, there is a sequence, and it is an arithmetic Progression with a = 1 and d = 4/3. Therefore, we can confirm that the original sequence is an Harmonic Progression.
(Note: "5" is nothing but 15/3)
In Harmonic Progression,

(we can also confirm that the numerator p and denominator q are relatively prime by prime factorising 8075)
So, p + q = 8078

By intuition and careful observation, one can guess that a possible value of x could be 2 (as 16 is given which is 2424 and we have no coefficient for x⁴).
So, the equation can be (x − 2)⁴ = x⁴ - 8x³ + 24x² - 32x + 16 where a = 24 and b = 32 which gives a - b = -8. (C)
Alternatively, the formula based approach would be:
For an equation of the form ax⁴ + bx³ + cx² + dx + e,
Sum of roots = -b/a, and
Product of roots = e/a.
Here, we have sum of roots as 8 and product of roots as 16.
As we can see the Arithmetic mean of the roots = Geometric mean of the roots. Hence, the roots must be equal. So the only root of the equation is 2.
Putting x = 2 in the equation will lead to (x − 2)⁴ = x⁴ - 8x³ + 24x² - 32x + 16 where a = 24 and b = 32 which gives a - b = -8. 

The correct response is (B). To find the "Average Rate" of the bus, we know we will need to find the Total Distance and the Total Time, so let's see how we can use the D = R x T formula to find the missing info.  
For the first part of the trip, we know that 30 miles = 15mph x T, so we know that T = 2 hours. For the middle part of the trip, we know that D = 10mph x 3 hours, so we know that D = 30 miles. For the last part of the trip, we know that 40 miles = R x 2 hours, so we know that R = 20mph.  
Now we can find the Total Distance and the Total Time. Total Distance = 30 miles + 30 miles + 40miles = 100 miles. Total Time = 2 hours + 3 hours + 2 hours = 7 hours. So the Average Rate = 100 miles/ 7 hours = 14.28mph. (B) is the closest approximation.

Given that:
x² + px + (1 - p) = 0
⇒ x₁ = 1 - p
Well,
⇒ (1 – p)² + p(1 – p) + (1 – p) = 0
(1 - p)(1 – p + p + 1) = 0
2(1 – p) = 0
⇒ p = 1
⇒ x² + x + 0 = 0
x(x + 1) = 0
x = -1, x = 0

Let work done by A in a day = 1/6
work done by B in a day = 1/8
work done by C in a day = 1/12
total work done by 3 of them in a day = 1/6 + 1/8 + 1/12
= (4 + 3 + 2)/24
= 9/24
Fraction of work done by C in a day = 2/9
fraction of total work by each of them will be same as the work done by each individual in a day.
Total earning on completion of job = 2340 $
C's share of earning = (2/9) * 2340
= 520$

What kind of numbers have exactly 3 factors?

Any positive integer will have '1' and the number itself as factors. That makes it a minimum of 2 factors (except '1' which has only one factor). If the positive integer has only one more factor, then in addition to 1 and the number, the square root of the number should be the only other factor.

There are two key points in the above finding. The number has to be a perfect square. And the only factor other than 1 and the number itself should be its square root.

Therefore, if a positive integer has only 3 factors, then it should be a perfect square and it should be the square of a prime number.

How many numbers from {1, 2, 3, 4, .... 100} have exactly 3 factors?

Let us look at an example. 4 has the following factors: 1, 2, and 4 (exactly 3 factors). It is the square of '2' which a prime number.
Squares of numbers that are not prime numbers will have more than 3 factors. For instance, 36 is a perfect square. But it has 9 factors.

Number of squares of prime numbers from 1 to 100 that have exactly 3 factors are 4, 9, 25, and 49. i.e., 4 numbers

Step 1: Compute the total number of possibilities

Number of ways of selecting two distinct integers from the set of first 100 positive integers = 100C₂ ways.

Step 2: Compute the number of favourable outcomes

The product of two distinct numbers 'a' and 'b' will be 4 when one of the numbers is 1 and the other is 4. There is only one set that will result in this product.
The same holds good for the other 3 numbers as well. Product of two distinct numbers 'a' and 'b' will be 9 when one of the numbers is 1 and the other is 9 and so on.
Therefore, there are 4 outcomes in which the product of the two numbers will result in a number that has exactly 3 factors.

Step 3: Compute the required Probability

First of all notice that since only 40 athletes play defense, then the number of athletes that play both midfield and defense cannot possibly be greater than 40. Eliminate D and E.
{Total} = {defense} + {midfield} - {both} + {neither}
100 = 40 + 70 - {both} + {neither}
{both} = {neither} + 10.
Since the least value of {neither} is given to be 20, then the least value of {both} is 20 + 10 = 30. Eliminate A and B.

In the first bold statement, the agent predicts, or concludes, that occupancy rates will increase despite decreasing population. The second bold statement describes the reasoning behind this prediction: if potential home-buyers are discouraged by high-interest rates on mortgages, they will opt to rent instead. So, the first statement is a prediction, and the second statement supports this prediction.

(A) The second statement does not weigh against the conclusion but rather supports it.

(B) The agent’s final prediction is made in the first bold statement, not the second bold statement.

(C) The first bold statement does not describe a pattern of cause and effect. In fact, it predicts the disjointed relationship between population and occupancy rates: as the population decreases, occupancy rates will increase.

(D) CORRECT. This choice describes the correct relationship between the two statements: the first is the conclusion, and the second supports this conclusion.

(E) The first statement is not an undisputed fact, but rather a prediction.

(A) Yes. That better training of anesthetists improved safety in no way implies that new equipment would not have a similar result. The argument cannot validly make a conclusion about equipment that was not studied.

(B) No. The argument is not circular. In fact, the argument is flawed because it takes too big of a leap in logic.

(C) No. The passage does not argue that the absence of a certain factor (monitoring devices) caused a certain result (increase in safety). Rather, it states that the presence of better-trained anesthetists resulted in a better safety record. The argument then invalidly concludes that the presence of the monitoring devices
would not also improve the safety record.

(D) No. Only one piece of evidence is cited—a review of hospital fatalities due to anesthesia during the last 20 years. No evidence is cited to support the conclusion regarding the use of monitoring equipment.

(E) No. The argument states that one event (better training of anesthetists) resulted in another event (an improved safety record in hospital anesthesia use).
Nothing in the passage suggests that both of these results were independently caused by a third event.

The passage mentions that the post-career average for 5-star players is 4.46, which is lower than their initial 5-star ranking. This suggests that the ranking system does not effectively judge high-end talent, as the most elite players are not able to surpass their initial high ranking.

Option (B) addresses this problem by pointing out that a five-star scale may not adequately account for the potential for elite players to overperform their initial ranking. The scale might not provide enough granularity to distinguish between the very best players, leading to a situation where players with tremendous careers still have post-career averages slightly below the maximum rating.

The other options (A, C, D, and E) introduce potential issues related to judging players, but they do not directly address the problem of the ranking system limiting the ability of the most elite players to surpass their initial ratings, as stated in the passage. Therefore, option (B) is the most appropriate choice.

A. Incorrect.

To solve this conclusion-weakening question, first, break down the argument. The first two sentences are premises which provide factual data; the last sentence includes a conclusion word (hypothesized) so it's the conclusion:

Premise A: A serious illness is hereditary (carried by genes transferred from parents to children)
      +
Premise B: half of those who have the disease have a parent who also has it
      =
Conclusion: half the children of a parent who has the disease will have it

Possible assumption: the ratio from Premise B, although it refers to a group of sick people only, can be also applied to the ratio of sick to healthy children in a family.

You are required to find data that weakens the hypothesis that parents give half their children the disease. The correct answer could be one that exposes the argument's assumption.

This answer choice neither weakens nor strengthens the conclusion, as the scientist claimed the disease has a 50% chance of transferring to one's children, rather than 100%. The prevalence of a 100% hereditary disease is irrelevant.

B. Those suffering from the disease whose parents also suffer from it have, on average, one other sick sibling and three healthy siblings.

This answer choice weakens the scientist's conclusion by providing contradicting evidence: if the average family of a sick parent has 2 sick children and 3 healthy children, the chances of a parent giving the disease to their children is not 50% (it's 2/5, or 40%).

C. Incorrect.
The treatability of an illness has nothing to do with the percentage of children of a person with the illness who will inherit it, which is the conclusion you are asked to weaken.

D. Incorrect.
This answer choice neither weakens nor strengthens the conclusion. The number of children a person has on average doesn't affect the chance of a sick person giving the illness to his child.

E. Incorrect.
This answer choice strengthens the conclusion. If 50% of someone's children have the disease, it follows that 25% of those children's children will also suffer from it (considering no-one else has the disease), so this answer choice is consistent with the conclusion, giving it some validity.

(A) This choice distorts the meaning of the passage. While the last paragraph notes that film audiences are more diverse, this is not connected to the information provided about Apocalypse Now Redux.

(B) CORRECT. The last paragraph notes that the extra footage was not originally included because it might repel audiences. Thus, the updated film's portrayal of war must be less appealing and more ambiguous than that of the original.

(C) This choice indicates a change in the opposite direction; the last paragraph indicates that the additional footage made the film's perspective on war harsher as opposed to more glorified.

(D) The passage indicates that not all war movies had the same tone, and the answer choice does not specify which "other movies" are referred to; therefore, this choice is incorrect.

(E) There is no mention of any removed footage in the passage. As it is not possible to know if any footage was removed, this choice is incorrect.

(A) In the last paragraph, Jarhead is listed as a film that was made years after the conflict it portrayed and had an ambivalent attitude to its topic. Thus, it can be inferred that it would resemble All Quiet on the Western Front. Remember that any information gleaned from seeing the film is outside knowledge. If this information cannot be deduced from the passage, it cannot be used to answer a question.

(B) In the third paragraph, Apocalypse Now is listed as a film that was made years after the conflict it portrayed and had an ambivalent attitude to its topic. Thus, it can be inferred that it would resemble All Quiet on the Western Front.

(C) In the second paragraph, The Bridge on the River Kwai is described as a film that was made years after the conflict it portrayed and showed the moral confusion of war. Thus, it can be inferred that it would resemble All Quiet on the Western Front.

(D) In the third paragraph, Platoon is described as a film that was made years after the conflict it portrayed and had an ambivalent attitude to its topic. Thus, it can be inferred that it would resemble All Quiet on the Western Front.

(E) CORRECT. In both the second and third paragraphs, Guadalcanal Diary is mentioned as a film made in wartime. In the second paragraph, it is listed as an example of a film that portrayed the “’the ultimate sacrifice’ as a noble and undoubted good.” In contrast, the first paragraph states that “All Quiet on the Western Front put forth an anti-war message by displaying the horrors of combat.” Thus, Guadalcanal Diary must be the portrayal of combat that least resembles that in All Quiet on the Western Front.

The passage clearly enunciates in the first paragraph that it plans to illustrate the cyclical pattern of the tone of Hollywood war movies. The second and third paragraphs trace the pattern's history through the last century, and then the passage ends by returning to the resilience of that cycle. Thus, the main point of the passage must reference establishing and describing the recurring pattern over time.

(C) CORRECT. This choice reiterates the theme that a pattern is durable, despite the doubts of some during "those days of social change" -- i.e., the late 1960's. This choice exactly mirrors the structure of the passage, which makes this point, provides historical evidence, and then reiterates that the pattern continues to endure.

A. An unrelated survey of annual charitable giving finds that residents of rural areas give 3% less to charity than residents of urban areas.
This supports the conclusion, which states that urban dwellers are more generous. Even if in this particular case urban dwellers donated more, this additional info supports the hypothesis that urban residents are in fact more generous.
B. There are more homeless people in urban areas than rural areas, making it more likely that urban residents would contribute to those charities.
Since the program in the passage is about homeless people, urban residents are more likely to donate to that cause. But we cannot generalize by saying that they are more generous in general. This weakens the conclusion.
C. There are more charities in general operating in urban areas than in rural areas.
This could translate in more opportunities to donate, and in this case, urban dwellers could donate more not because they are generous, but because they have more possibilities to do so.
D. The survey is calculated based on dollar amount rather than percentage of income and does not account for the fact that incomes in urban areas are often higher.
The first part (before the comma) points out that the dollar amount is not a good estimator of generosity compared to a percentage indicator.
The second part gives credit to the fact that, because incomes in the urban area are higher, the "15 $ difference" should not translate into more generosity.
E. The group Live in the City has been known to alter survey results for marketing purposes.
Since the group is an "urban-promotion group" it could alter the results in favour of the city.

The passage suggests several ways in which dogs are superior to human methods of detecting seizures. We don't know how dogs can detect seizures, but we know some things about their behaviour when they do detect seizures, and we know they can do so even when in another room. We also find out that epileptics do not display any number of "noticeable" changes before undergoing a seizure.

Consider each choice, looking for a reasonable inference:

(A) The passage says nothing about the accuracy of prediction, so this is not a reasonable inference.

(B) The passage is limited to information about seizures, so we know nothing about heart attack detection.

(C) This is one possible explanation of dogs' seizure detection abilities, but it is not supported by the passage, since there are other ways in which dogs might detect the onset of a seizure.

(D) This is correct. It is based directly on the information that dogs do not have to be in the same room as a patient. We don't know how they detect the onset of a seizure, but we know it isn't reliant on visual information.

(E) This choice reverses causality. The dog stares intently in response to the onset of a seizure; the seizure does not occur because the dog stares intently.