All India GMAT Group

Is (2y+z)(3x)(5y)(7z) < (90y)(14z)?
1. y and z are positive integers; x = 1
2. x and z are positive integers; y = 1
  • a)
    Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;
  • b)
    Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion asked;
  • c)
    BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;
  • d)
    EACH statement ALONE is sufficient to answer the question asked;
  • e)
    Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked,and additional data are needed. 
Correct answer is option 'A'. Can you explain this answer?

Notes Wala answered  •  21 hours ago
Simplify the equation:
Is (2y+z)(3x)(5y)(7z) < (90y)(14z)?
Simplified: is (2y+z)(3x)(5y)(7z) < ((2*5*3*3)y)((7*2)z)?
Simplified: is (2y+z)(3x)(5y)(7z) < (2y)(5y)(32y)(7z)(2z)?
Simplified: is (2y+z)(3x)(5y)(7z) < (2y+z)(5y)(32y)(7z)?
Cancel out 2y+z, 5y, and 7z
Simplified: is 3x < 32y?
Evaluate Statement (1) alone.
Statement (1) says that x = 1. So, plug that information in and work from there.
Simplified Question: is 31 < 32y where y is a positive integer?
Further Simplified: is 1 < 2y where y is a positive integer?
At this point, some students can see that Statement (1) is SUFFICIENT. However, a more thorough analysis is provided just to be clear.
Since x and y are given as positive integers, the smallest possible value for y is 1. In this case 1 < 2(1). Since the inequality held true when y=1, it will hold true for any legal value of y since y will only get larger and x will not change.
Thus, 3x will always be less than 32y.
Statement (1) is SUFFICIENT.
Evaluate Statement (2) alone.
Statement (2) says y = 1 and x and z are positive integers. So, plug that information and work from there.
Is 3x < 32(1)?
Or: is 3x < 32?
Or: is x < 2?
Since the only restriction on x is that it is a positive integer, x could be 1 (in which case the inequality would be true and the answer to the question would be "Yes") or, x could be 2 (in which case the inequality would not be true and the answer to the question would be "No").
Since different answers to the question "is x < 2?" are possible, there is no definitive answer to the question. Statement (2) is NOT SUFFICIENT.
Since Statement (1) alone is SUFFICIENT and Statement (2) alone is NOT SUFFICIENT, answer A is correct.

ohn is trying to get from point A to point C, which is 15 miles away directly to the northeast; however the direct road from A to C is blocked and John must take a detour. John must travel due north to point B and then drive due east to point C. How many more miles will John travel due to the detour than if he had traveled the direct 15 mile route from A to C?
1. Tha ratio of the distance going north to the distance going east is 4 to 3
2. The distance traveled north going the direct route is 12
  • a)
    Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;
  • b)
    Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion asked;
  • c)
    BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;
  • d)
    EACH statement ALONE is sufficient to answer the question asked;
  • e)
    Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked,and additional data are needed. 
Correct answer is option 'D'. Can you explain this answer?

Notes Wala answered  •  21 hours ago
Draw a diagram of the problem with the information from the question:

AC = 15
You are dealing with a right-triangle since a right angle will be formed by going straight north and then turning straight east.
Evaluate Statement (1) alone.
Translate the information from Statement (1) into algebra:
(AB)/(BC) = 4/3
3(AB) = 4(BC)
Set up a Pythagorean theorem equation:
(AB)2 + (BC)2 = (AC)2
(AB)2 + (BC)2 = (15)2
You now have two equations and two unknowns:
Equation (1): (AB)2 + (BC)2 = (15)2
Equation (2): 3(AB) = 4(BC)
With two unique equations and two unknowns, a solution must exist. With this solution, you can subtract 15 from the detour distance and arrive at an answer.
Statement (1) is SUFFICIENT.
Note: You should not do these calculations on the test since they are not necessary for determining sufficiency. However, to demonstrate that there is a solution, we show how you would arrive at a numerical answer:
(AB)2 + (BC)2 = (15)2
(AB)2 + (.75AB)2 = (15)2
{rearrange Equation 2, solving for BC and substitute in BC=.75AB}
(AB)2(1 + .752) = 225 {factor out (AB)2}
(AB)2 = 144
AB = 12
Substitute Back into Equation 2:
3(12) = 4(BC)
BC = 9
With these two distances, you can calculate the distance traveled on the detour.
Direct Route: 15
Detour: 9 + 12 = 21
Extra Distance: 21 - 15 = 6
Evaluate Statement (2) alone.
Set up a Pythagorean theorem equation:
(AB)2 + (BC)2 = (AC)2
(AB)2 + (BC)2 = (15)2
You are told that AB = 12. Substitute this information in and solve for BC.
(12)2 + (BC)2 = (15)2
(BC)2 = 81
BC = 9
Statement (2) is SUFFICIENT.
Note: You should not do these calculations on the test since t
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What is the approximate amount that should be invested today at an annual rate of 10% compounded semi-annually so that an amount of $1000 is received at the end of the first year?
  • a)
    $830
  • b)
    $890
  • c)
    $910
  • d)
    $970
  • e)
    $990
Correct answer is option 'C'. Can you explain this answer?

Aditya Sharma answered  •  yesterday
Understanding the Problem
To determine how much needs to be invested today to receive $1000 at the end of one year, we need to account for the effect of compound interest. We are given:
- Future Value (FV) = $1000
- Annual Interest Rate (r) = 10%
- Compounding Frequency = Semi-Annually (2 times a year)
Calculating the Effective Interest Rate
The effectiv
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­­A shopper bought a tie and a belt during a sale. Which item did he buy at the greater dollar value?
(1) He bought the tie at a 20 percent discount.
(2) He bought the belt at a 25 percent discount
  • a)
    Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
  • b)
    Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
  • c)
    BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
  • d)
    EACH statement ALONE is sufficient to answer the question asked.
  • e)
    Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'E'. Can you explain this answer?

Dipanjan Mehra answered  •  yesterday
Understanding the Problem
To determine which item (tie or belt) was purchased at a greater dollar value, we need to analyze the information provided in each statement regarding their discounts.
Statement (1): Tie at 20% Discount
- The tie is discounted by 20%, but we do not know the original price of the tie.
- Without the original price, we cannot ascertain its f
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n is an integer. What is the units digit of n5 − 5n3 + 4n ?
  • a)
    0
  • b)
    2
  • c)
    4
  • d)
    6
  • e)
    8
Correct answer is option 'A'. Can you explain this answer?

Sandeep Mehra answered  •  yesterday
Understanding the Expression
To find the units digit of the expression n^5 − 5n^3 + 4n, we can evaluate it for different values of n and look for a pattern. The units digit of a number is the digit in the ones place, which can be found by taking the number modulo 10.
Calculating Units Digits
Let's break down the expression for n = 0 to 9 and find the units digit for ea
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If the remainder is 5 when x is divided by 101, what is the remainder when x3+x2+x is divided by 101?
  • a)
    5
  • b)
    6
  • c)
    31
  • d)
    54
  • e)
    55
Correct answer is option 'D'. Can you explain this answer?

Nandita Chauhan answered  •  2 days ago
Understanding the Problem
To solve for the remainder of the expression x³ + x² + x when x is divided by 101, we start by noting the given condition:
- The remainder when x is divided by 101 is 5.
This means we can express x in the form:
- x = 101k + 5 for some integer k.
Substituting the Value of x
Now, we substitute this value of x into the expression
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Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 4 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex?
  • a)
    R – 4
  • b)
    R / (R + 4)
  • c)
    R / (R – 8)
  • d)
    8 / (R – 8)
  • e)
    R2 – 4
Correct answer is option 'C'. Can you explain this answer?

Nikhil Khanna answered  •  3 days ago
Understanding the Problem
Alex walks away from Brenda at 4 miles per hour. After one hour, Brenda rides in the opposite direction at R miles per hour, where R > 8. We need to determine the time Alex has been walking when Brenda has covered twice the distance Alex has.
Distance Formulas
- Distance covered by Alex:
If Alex walks for T hours, his distance is
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The most important concern in the minds of social media users is the protection of their privacy. Accordingly, as per the privacy policy released to customers, most social media companies use the latest 256-bit encryption techniques to transmit and store user data. However, recent tests done by several security companies show that 128-bit encryption is sufficient for all practical purposes.  Hence, if data security is the only objective, then by switching to the older and cheaper 128-bit encryption, media companies can increase their overall profits without compromising on the security of user data. 
Which of the following, if true, argues against the suggested change in the encryption techniques?
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Manasa Gupta answered  •  3 days ago
Understanding the Argument Against Switching Encryption Techniques
The suggestion to switch from 256-bit to 128-bit encryption is based on the idea that security is sufficient and cost savings can be achieved. However, option 'E' highlights a critical concern that counters this change.
Customer Perception of Security
- Downgrade of Security Features: Customer su
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At a technology consulting firm with x computers, all of which are desktops or laptops, 30% are laptops; if 80% of the total number of computers have more than 1GB of RAM and 10% of the computers with less than 1GB of RAM are laptops (and no computers have exactly 1GM of RAM), approximately what percent of the desktops have more than 1GB of RAM?
  • a)
    75%
  • b)
    60%
  • c)
    52%
  • d)
    40%
  • e)
    45%
Correct answer is option 'A'. Can you explain this answer?

Disha Mehta answered  •  3 days ago
Understanding the Problem
To solve the problem, we need to analyze the distribution of computers based on their types and RAM capacity.
Given Data
- Total computers (x): Desktops + Laptops
- Laptops: 30% of x
- Desktops: 70% of x
- Computers with more than 1GB RAM: 80% of x
- Laptops with less than 1GB RAM: 10% of computers with less than 1GB RAM... more

Jake invests $5000 at 10% simple annual interest and another amount of money at x percent simple interest. What amount of money did Jake invests at x percent interest?
(1) The total amount of interest earned on all investments at the end of one year is $800.
(2) x = 6%.
  • a)
    Statements (1) and (2) TOGETHER are not sufficient.
  • b)
    Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient.
  • c)
    Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  • d)
    Each Statement ALONE is sufficient.
  • e)
    Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient.
Correct answer is option 'C'. Can you explain this answer?

Sanskriti Ahuja answered  •  4 days ago
Understanding the Problem
Jake invests $5000 at a 10% simple annual interest rate, and another unknown amount at x% interest. We need to determine the amount invested at x% given the total interest earned after one year is $800.
Analyzing Statement (1)
- The total interest earned from both investments is $800.
- Interest from the first investment:
Interest
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Directions: Each of these sentence correction practice questions presents a sentence, some or all of which is underlined. Below the sentence you will find five ways of phrasing the underlined part. Option A always repeats the original phrasing, while the other four are different. Choose the answer that produces the most effective sentence based on the requirements of standard written English. Your answer should make the sentence clear, exact, and grammatically correct.
Q. Once the computer generates the financial reports, they are then used to program a company-wide balance sheet, named the way it is named because it demonstrates that every department’s accounting elements are in balance.
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Prateek Gupta answered  •  2 weeks ago
Analysis of the Sentence
The original sentence is convoluted and contains unnecessary phrases that detract from clarity.
Issues in the Original Sentence
- Ambiguity: The phrase "named the way it is named" is redundant and confusing.
- Pronoun Reference: The sentence uses "they" and "it" without clear antecedents, leading to confusion about what thes
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The important parts of any university professor’s job include not only classroom teaching but also research, publication, and lectures to colleagues and the public. This is why university professors who are good classroom teachers but have not engaged in any other scholarly activities are usually denied tenure.
The statements above, if true, most strongly support which one of the following?
  • a)
    University professors who have not failed to perform important parts of their jobs are not usually denied tenure.
  • b)
    Some university professors have been denied tenure even though they have done an important part of their jobs well.
  • c)
    University professors who do not engage in other scholarly activities are usually good classroom teachers.
  • d)
    University professors who have engaged in research, publication, and lectures to colleagues and the public are usually granted tenure.
  • e)
    Classroom teaching is the least important part of a university professor’s job
Correct answer is option 'B'. Can you explain this answer?

Ruchi Pillai answered  •  2 weeks ago
Understanding the Argument
The argument highlights that university professors must engage in various scholarly activities—beyond classroom teaching—to secure tenure. If they excel in teaching but neglect research, publication, and public lectures, they face denial of tenure.
Analysis of Options
- a) This option suggests that professors who perform all job parts
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Directions: Each of these critical reasoning practice questions are based on a short argument, a set of statements, or a plan of action. For each question, select the best answer of the choices given.
Botanist: The Lady’s Slipper is a type of orchid that requires bright light, but no direct sun, relatively consistent room temperature, and water no more than twice a month for maximum growth. Our newest greenhouse comes with a watering system that has been tested with the Lady’s Slipper orchids, and can be programmed to release water onto the orchids once every two weeks. The new greenhouse is already capable of maintaining a constant room temperature and blocking out direct sunlight, so we can confidently state the new greenhouse is ideal for their growth.
Q. Which of the following is an assumption required by the botanist’s conclusion?
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Ruchi Pillai answered  •  2 weeks ago
Understanding the Botanist's Conclusion
The botanist concludes that the new greenhouse is ideal for the growth of Lady’s Slipper orchids based on specific features of the greenhouse and the needs of the orchids.
Key Assumptions in the Conclusion
To support this conclusion, certain assumptions must be made. Here’s a breakdown:
- Watering System's Functionality<
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Directions: Each of these critical reasoning practice questions are based on a short argument, a set of statements, or a plan of action. For each question, select the best answer of the choices given.
According to a recent census, West Egg had more mansions per capita last year than East Egg, while East Egg had slightly fewer residents than West Egg. Since the census, West Egg and East Egg have each seen the demolition of a dozen dilapidated mansions within their respective borders, and no new mansions have begun construction. It must be true, therefore, that _________.
Q. Which of the following best completes the passage?
  • a)
    West Egg and East Egg both have more cared-for mansions than dilapidated mansions.
  • b)
    West Egg has more mansions than East Egg.
  • c)
    West Egg has more mansions per capita than East Egg.
  • d)
    West Egg and East Egg have the same number of mansions.
  • e)
    West Egg has more residents than East Egg.
Correct answer is option 'B'. Can you explain this answer?

Ruchi Pillai answered  •  2 weeks ago
Understanding the Argument
The argument presents a comparison between West Egg and East Egg based on the number of mansions and population. Key points from the argument include:
- West Egg had more mansions per capita than East Egg.
- East Egg had slightly fewer residents than West Egg.
- Both locations experienced the demolition of a dozen dilapidated mansions, with no
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Directions: Each of these critical reasoning practice questions are based on a short argument, a set of statements, or a plan of action. For each question, select the best answer of the choices given.
Many of the yachts anchored in Cannes boast a luxurious Jacuzzi on their uppermost deck. Almost 80% of the yachts that were sold in the past ten years in Cannes are older models, and none of them had built-in Jacuzzis.
Q. The information above most strongly supports which of the following?
  • a)
    Only new yacht-models come with Jacuzzis.
  • b)
    None of the newer yacht-models with Jacuzzis will be sold in the next ten years.
  • c)
    All yachts in Cannes without Jacuzzis were sold in the past ten years.
  • d)
    People shopping for yachts will likely choose an older-model with a Jacuzzi than an older-model without a Jacuzzi.
  • e)
    Some newer yacht-models were sold in the past ten years in Cannes.
Correct answer is option 'E'. Can you explain this answer?

Ruchi Pillai answered  •  2 weeks ago
Understanding the Argument
The argument presents the following key points:
- Many yachts in Cannes have Jacuzzis.
- 80% of yachts sold in the past decade are older models, none of which have Jacuzzis.
Analyzing the Options
Now, let's evaluate the given answer choices:
Option A: Only new yacht-models come with Jacuzzis.
- This is a strong clai
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Directions: Each of these critical reasoning practice questions are based on a short argument, a set of statements, or a plan of action. For each question, select the best answer of the choices given.
Though the Great Fakir is a well-respected illusionist and escape artist, he has recently become outspokenly critical of the performance act of the Magnificent Mystic, calling it largely staged and fake. The Magnificent Mystic’s stage act involves a “Buried Alive” set-piece, wherein he appears to be placed in a coffin which is then wrapped in chains, and lowered into a make-shift grave, only to reappear from the side of the stage after several minutes. The Great Fakir criticized the Magnificent Mystic’s act in an editorial as “an obvious form of mechanical trickery,” but the Great Fakir’s own world-famous performance act uses mechanical devices such as boxes, ladders, and glass panes to create his own stage illusions, which have helped him become the world’s most popular touring magician.
Q. The argument's reasoning is most open to criticism on the basis that it:
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Ruchi Pillai answered  •  2 weeks ago
Understanding the Argument
The argument critiques the performance of the Magnificent Mystic while highlighting the Great Fakir's use of similar techniques. The key issue is the inconsistency in the Great Fakir's stance.
Critical Analysis of Option E
The correct answer is option 'E', which suggests that the Great Fakir's criticism implies there is no difference between
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David: Humans did not evolve from an aquatic ancestor. Chimpanzees, our closest living relatives, share over 98 percent of our DNA, and they don’t swim or spend time in the water unless they have to. They even use leaves to soak up water to drink, rather than cup their hands.
Lynn: True, but we also have a layer of fat under our skin, which would make us unique in the animal kingdom as the only non-aquatic species that has evolved such fat, not to mention that fatty tissue is 90 percent as dense as water, helping us float and thereby conferring a survival advantage that would be useless outside of water.
Lynn responds to David’s argument by
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Nayanika Bajaj answered  •  2 weeks ago
Understanding Lynn's Response
Lynn's response to David's argument showcases a nuanced approach to the discussion about human evolution. Here’s a breakdown of why option 'E' is the correct answer.
Acknowledgment of Facts
- Lynn recognizes the validity of David's points regarding human evolution and the similarities with chimpanzees.
- She accepts that David present
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Directions: Each of these critical reasoning practice questions are based on a short argument, a set of statements, or a plan of action. For each question, select the best answer of the choices given.
Although Apple products have continued to enjoy record-breaking profits worldwide, iPod retailers have recently reported that the numbers of the touch-screen devices sold have steadily decreased in the past two years. However, in the past two years, the numbers of iPhones sold have nearly doubled. Thus, more people are choosing to buy iPhones than iPods when selecting from Apple’s products.
Q. The reasoning in the argument is questionable primarily because the argument:
  • a)
    assumes an inherent preference in people for one product over another.
  • b)
    lacks specific numbers to bolster the conclusion.
  • c)
    doesn’t admit alternative explanations for the situation.
  • d)
    suggests iPod retailers and iPhone retailers are one and the same.
  • e)
    limits the scope of its argument to only two of Apple’s products.
Correct answer is option 'C'. Can you explain this answer?

Nayanika Bajaj answered  •  2 weeks ago
Understanding the Argument
The argument presents a scenario where iPod sales are declining while iPhone sales are increasing, leading to the conclusion that consumers prefer iPhones over iPods. However, this reasoning has flaws.
Key Flaw in the Reasoning
The correct answer is option 'C', which states that the argument "doesn't admit alternative explanations for the sit
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Jyoti Nair asked a question

Each of the 10 persons namely A, Q, R, Z, M, N, P, B, K and L are wearing a shirt. The colour of each shirt is one out of blue, green and red. There are ten chairs placed in a row. The chairs are consecutively numbered 1, 2, 3, 4...9 and 10 from left to right in that order. These ten persons have to sit on the chairs such that there is only one person in each chair. The number of persons wearing a green and a blue shirt is 2 and 3 respectively.
Additional Information:
1. No two persons wearing blue shirts sit on consecutively numbered chairs.
2. Among the persons wearing red shirts, exactly three persons always are sitting together while the remaining two never.
3. A person wearing a blue shirt and a person wearing a green shirt never is sitting on consecutively numbered chairs.
4. A person wearing a green shirt cannot sit on chairs numbered 2 or 9.
5. Persons wearing red shirts are not sitting at extreme ends.
The following table provides information about the six different seating arrangements namely I, II, III, IV, V and VI of the ten persons done by Mr. Crazy. He observed that out of all the seating arrangements done by him, there is one arrangement that is not consistent with the information stated under "Additional Information".
Q. Which of the arrangements done by Mr. Crazy is not consistent with the information stated under "Additional Information"?
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