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MathRevolution
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 25 Jun 2021, 21:58
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Que: If ‘p’ and ‘q’ are integers, what is the value of q?

(1) \(\frac{q}{p} = \frac{2}{3}\).

(2) \(q> 0\) and \(p > 0.\)
Show more


Solution: To save time and improve accuracy on DS questions in GMAT, learn and apply the Variable Approach.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Visit https://www.mathrevolution.com/gmat/lesson for details.

Now we will solve this DS question using the Variable Approach.

Let’s apply the 3 steps suggested previously.

Follow the first step of the Variable Approach by modifying and rechecking the original condition and the question.

We have to find the value of q.

Follow the second and the third step: From the original condition, we have 2 variables (p and q). To match the number of variables with the number of equations, we need 2 equations. Since conditions (1) and (2) will provide 1 equation each, C would most likely be the answer.

Recall 3- Principles and Choose C as the most likely answer.

Let’s look at both conditions together.

Condition (1) tells us that \(\frac{q}{p} = \frac{2}{3}\) , and Condition (2) tells us that p> 0 and q > 0.

Number of possible cases for \(\frac{q}{p}\) such that ratio is 2:3 are

=> q = 2 and p = 3 (q > 0, p > 0)

=> q = 4 and p = 6 (q > 0, p > 0)

=> q = 6 and p = 9 (q > 0, p > 0)

And so on…

The answer is not a unique value; both conditions combined are not sufficient according to Common Mistake Type 2 which states that the answer should be a unique value.

Both conditions together are not sufficient.

Therefore, E is the correct answer.

Answer: E
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 25 Jun 2021, 22:05
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Que: The cost of a certain phone call was $2 for the first 2 minutes and $0.10 for each additional minute after the first 2 minutes. Did the phone call last longer than 10 minutes?

(1) The cost of the phone call was less than $3.00.
(2) The cost of the phone call was greater than $3.00.
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 27 Jun 2021, 21:03
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Que: The cost of a certain phone call was $2 for the first 2 minutes and $0.10 for each additional minute after the first 2 minutes. Did the phone call last longer than 10 minutes?

(1) The cost of the phone call was less than $3.00.
(2) The cost of the phone call was greater than $3.00.
Show more


Solution: To save time and improve accuracy on DS questions in GMAT, learn and apply the Variable Approach.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Visit https://www.mathrevolution.com/gmat/lesson for details.

Now we will solve this DS question using the Variable Approach.

Let’s apply the 3 steps suggested previously.

Follow the first step of the Variable Approach by modifying and rechecking the original condition and the question.

We have to find whether the call cost longer than 10 minutes.

A 10- minute call will cost as: cost of 2 minutes + cost of 8 minutes = $2 + 8($0.10) = $2.80

We have to find did the call cost more than $2.80?

Condition (1) tells us that the cost of the phone call was less than $3.00.

If call cost = $2.70, then we get NO as an answer.
But If call cost = $2.90, then we get YES as an answer.

The answer is not a unique YES or a NO; condition (1) alone is not sufficient according to Common Mistake Type 1 which states that the answer should be a unique YES or a NO.

Condition (2) tells us that the cost of the phone call was greater than $3.00.

This implies that the cost of the call will always be greater than $2.80 - YES

The answer is a unique YES; condition (2) alone is sufficient according to Common Mistake Type 1 which states that the answer should be a unique YES or a NO.

Condition (2) alone is sufficient.

Therefore, B is the correct answer.

Answer: B
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 27 Jun 2021, 21:12
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Que: What is the standard deviation of four numbers a, b, c, and d?

(1) Sum of a, b, c, and d is 30.
(2) Sum of squares of a, b, c, and d is 238.
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 29 Jun 2021, 22:07
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Que: What is the standard deviation of four numbers a, b, c, and d?

(1) Sum of a, b, c, and d is 30.
(2) Sum of squares of a, b, c, and d is 238.
Show more


Solution: To save time and improve accuracy on DS questions in GMAT, learn and apply the Variable Approach.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Visit https://www.mathrevolution.com/gmat/lesson for details.

Now we will solve this DS question using the Variable Approach.

Let’s apply the 3 steps suggested previously.

Follow the first step of the Variable Approach by modifying and rechecking the original condition and the question.

We have to find ‘S.D. of a, b, c, and d.

S.D. = \( \sqrt{((mean of squares of numbers)-(square of mean of numbers))}\)

Follow the second and the third step: From the original condition, we have 4 variables (a, b, c, and d). To match the number of variables with the number of equations, we need 4 equations. Since conditions (1) and (2) will provide 1 equation each, E would most likely be the answer.

Recall 3- Principles and Choose E as the most likely answer. Let’s look at both conditions together.

Condition (1) tells us that the sum is 30.

Condition (2) tells us that the sum is 238.

From 1st: Mean = 7.5 and square of mean = \(56.25\)

From 2nd: Mean of squares of numbers = \(\frac{238}{4} = 59. 5\)

Thus, S.D. \(= \sqrt{((mean of squares of numbers)-(square of mean of numbers))}\)

S.D. \(= \sqrt{(59.5-56.25=3.25≈3)} = 1.732\)

The answer is unique, so the conditions combined are sufficient according to Common Mistake Type 2 which states that the answer should be a unique value.

Both conditions together are sufficient.

Therefore, C is the correct answer.

Answer: C
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 29 Jun 2021, 22:14
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Que: If the product of two distinct integers’ p and q is 60, what is p?

(1) p is an odd integer.
(2) p > q.
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 02 Jul 2021, 20:40
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Que: If the product of two distinct integers’ p and q is 60, what is p?

(1) p is an odd integer.
(2) p > q.
Show more


Solution: To save time and improve accuracy on DS questions in GMAT, learn and apply the Variable Approach.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Visit https://www.mathrevolution.com/gmat/lesson for details.

Now we will solve this DS question using the Variable Approach.

Let’s apply the 3 steps suggested previously.

Follow the first step of the Variable Approach by modifying and rechecking the original condition and the question.

We have to find the value of p – where ‘p’ and ‘q’ are integers and p * q = 60.

Follow the second and the third step: From the original condition, we have 2 variables (p, and q) and 1 equation (p * q = 60). To match the number of variables with the number of equations, we need 1 more equation. Since conditions (1) and (2) will provide 1 equation each, D would most likely be the answer.

Recall 3- Principles and Choose D as the most likely answer. Let’s look at each condition.

Condition (1) tells us that p is an odd integer.

For p * q = 60, where ‘p’ is odd - we can have the following possible combinations

=> p = 5 and q = 12 – p is odd.

=> p = -5 and q = -12 – p is odd.

=> p = 3 and q = 20 – p is odd.

=> p = -3 and q = -20 – p is odd.

The answer is not unique, so Condition (1) alone is not sufficient according to Common Mistake Type 2 which states that the answer should be a unique value.

Condition (2) tells us that p > q.

For p * q = 60, where ‘p > q’ - we can have following possible combinations

=> p = 10 and q = 6 – p > q [Also p = -6 and q = -10].

=> p = 15 and q = 4 – p > q [Also p = -4 and q = -15].

=> p = 20 and q = 3 – p > q [Also p = -3 and q = -20].

The answer is not unique, so Condition (2) alone is not sufficient according to Common Mistake Type 2 which states that the answer should be a unique value.

Let’s look at both conditions combined:

For p * q = 60, where ‘p > q’ and ‘p’ is odd - we can have the following possible combinations

=> p = 15 and q = 4 – p > q and ‘p’ is odd.

=> p = -3 and q = -20 – p > q and ‘p’ is odd.

The answer is not unique, so conditions combined are not sufficient according to Common Mistake Type 2 which states that the answer should be a unique value.

Both conditions together are not sufficient.

Therefore, E is the correct answer.

Answer: E
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 02 Jul 2021, 20:48
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Que: Is ‘a’ an integer?

(1) \(a^4\) is an integer.
(2) \(4a\) is an integer.
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 12 Jul 2021, 23:21
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Que: Is ‘a’ an integer?

(1) \(a^4\) is an integer.
(2) \(4a\) is an integer.
Show more

Solution: To save time and improve accuracy on DS questions in GMAT, learn and apply the Variable Approach.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Visit https://www.mathrevolution.com/gmat/lesson for details.

Now we will solve this DS question using the Variable Approach.

Let’s apply the 3 steps suggested previously.

Follow the first step of the Variable Approach by modifying and rechecking the original condition and the question.

We have to find whether ‘a’ is an integer.

Follow the second and the third step: From the original condition, we have 1 variable (a). To match the number of variables with the number of equations, we need 1 equation. Since conditions (1) and (2) will provide 1 equation each, D would most likely be the answer.

Recall 3- Principles and Choose D as the most likely answer. Let’s look at each condition separately.

Condition (1) tells us that the \(a^4\) is an integer.

=> If \(a^4 = 16\), then a = 2 - YES

=> But if \(a^4 = 4\), then a is not an integer - NO

The answer is not a unique YES or a NO, so Condition (1) alone is not sufficient according to Common Mistake Type 1 which states that the answer should be a unique value.

Condition (2) tells us that the 4a is an integer.

=> If a = 10, then 4a = 10 * 4 = 40.

=> But if a = 7.5, then 4a = 4 * 7.5 = 30.

The answer is not a unique YES or a NO, so Condition (2) alone is not sufficient according to Common Mistake Type 1 which states that the answer should be a unique value.


Let’s look at both conditions combined:

=> If \(a^4 = 16\), then a = 2 and then 4a = 4 * 2 = 8 is an integer – YES

=> If \(a^4 = 1\), then a = 1 and then 4a = 4 * 1 = 4 is an integer – YES

=> But if, \(a^4 = 4\), then a = 1.414 and then 4a = 4 * 1.414 = is not an integer

Only if ‘a’ is an integer then, \(a^4\) and \(4a\) will be an integer.

The answer is a unique value YES; both conditions combined are sufficient according to Common Mistake Type 1 which states that the answer should be a unique YES or a NO.

Both conditions together are sufficient.

Therefore, C is the correct answer.

Answer: C
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 12 Jul 2021, 23:28
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Que: If |x - 4| < 6, what is the value of x?

(1) \(x > -5\)
(2) \(x^2 + 4x + 3 = 0\)
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 13 Jul 2021, 21:45
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Que: If |x - 4| < 6, what is the value of x?

(1) \(x > -5\)
(2) \(x^2 + 4x + 3 = 0\)
Show more


Solution: To save time and improve accuracy on DS questions in GMAT, learn and apply the Variable Approach.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Visit https://www.mathrevolution.com/gmat/lesson for details.

Now we will solve this DS question using the Variable Approach.

Let’s apply the 3 steps suggested previously. [Watch lessons on our website to master these 3 steps]

Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question.

We have to find the value of ‘x’ when is |x - 4| < 6.

Since, |x - 4| < 6, then x - 4 < 6 or -6.

=> If x - 4 < 6, then x < 6 + 4 = 10

=> But if -6< x - 4 , then -6 + 4 = -2 < x or -2 < x < 10

We have to find the value of x.

Follow the second and the third step: From the original condition, we have 1 variable (x). To match the number of variables with the number of equations, we need 1 equation. Since conditions (1) and (2) will provide 1 equation each, D would most likely be the answer.
Recall 3- Principles and Choose D as the most likely answer. Let’s look at each condition separately.

Thus, look at condition (1) that tells us that x > -5.

=> x = -1 or 1

The answer is not unique; so condition (1) alone is not sufficient according to Common Mistake Type 2 which states that the answer should be a unique value.

Condition (2) tells us that \(x^2 + 4x + 3 = 0\).

=> \(x^2 + 4x + 3 = 0\)

=> (x + 1) (x + 3) = 0

=> x = -3 or -1, in this case, x=-1 (since -2 < x < 10)

The answer is unique; condition (2) alone is sufficient according to Common Mistake Type 2 which states that the answer should be a unique value

Condition (2) alone is sufficient.

Therefore, B is the correct answer.

Answer: B
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 13 Jul 2021, 21:51
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Que: If p and q are positive integers, what is the value of p?

(1) \(5^p + 7^q = 174. \)
(2) \(q = 2\)
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 14 Jul 2021, 21:22
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Que: If p and q are positive integers, what is the value of p?

(1) \(5^p + 7^q = 174. \)
(2) \(q = 2\)
Show more


Solution: To save time and improve accuracy on DS questions in GMAT, learn and apply the Variable Approach.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Visit https://www.mathrevolution.com/gmat/lesson for details.

Now we will solve this DS question using the Variable Approach.

Let’s apply the 3 steps suggested previously.

Follow the first step of the Variable Approach by modifying and rechecking the original condition and the question.

We have to find the value of ‘p – where ‘p’ and ‘q’ are positive integers.

Follow the second and the third step: From the original condition, we have 2 variables (p and q). To match the number of variables with the number of equations, we need 2 equations. Since conditions (1) and (2) will provide 1 equation each, C would most likely be the answer.

Recall 3- Principles and Choose C as the most likely answer. Let’s look at both conditions combined together.

Condition (1) tells us that \(5^p + 7^q = 174. \)

Condition (2) tells us that \(q = 2\)

=> \(5^p + 7^2 = 174. \)

=> \(5^p + 49 = 174\)

=> \(5^p = 174 - 49 = 125\)

=> \(5^p = 5^3\)

Therefore, p = 3

The answer is a unique value; both conditions combined together are sufficient according to Common Mistake Type 2 which states that the answer should be a unique value. So, C seems to be the answer.

However, since this question is an integer question, which is also one of the key questions, we should apply CMT 4(A), which means that if an answer C is found too easily, either A or B should be considered as the answer. Let’s look at each condition separately,

Let’s take each condition separately.

Condition (1) tells us that \(5^p + 7^q = 174. \)

Since the exponents of 5 would reach 174 faster than the exponents of 7, we need to try with the exponents of 5 so that we can get the answer(s) in the least possible trials.

If p = 3, then

=> \(5^3 + 7^q = 174\)

=> \(125 + 7^q = 174\)

=> \(7^q = 174 - 125 = 49= 72 \)

Therefore, p = 3

The answer is a unique value; condition (1) alone is sufficient according to Common Mistake Type 2 which states that the answer should be a unique value.

Condition (2) tells us that q = 2

=> But ‘p’ is still unknown

The answer is not a unique value; condition (2) alone is not sufficient according to Common Mistake Type 2 which states that the answer should be a unique value.

If the question has both C and A as its answer, then A is the answer rather than C according to the definition of DS questions.

Condition (1) alone is not sufficient.

Therefore, A is the correct answer.

Answer: A
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Que: If x and y are positive integers, is xy a multiple of 12?

(1) x is a multiple of 3.
(2) y is a multiple of x.
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 16 Jul 2021, 09:36
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Que: If x and y are positive integers, is xy a multiple of 12?

(1) x is a multiple of 3.
(2) y is a multiple of x.
Show more


Solution: To save time and improve accuracy on DS questions in GMAT, learn and apply the Variable Approach.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Visit https://www.mathrevolution.com/gmat/lesson for details.
Now we will solve this DS question using the Variable Approach.

Let’s apply the 3 steps suggested previously.

Follow the first step of the Variable Approach by modifying and rechecking the original condition and the question.

We have to find whether xy is a multiple of 12 – where ‘x’ and ‘y’ are positive integers.

=> xy = 12n – where ‘n’ must be an integer

Follow the second and the third step: From the original condition, we have 2 variables (x and y). To match the number of variables with the number of equations, we need 2 equations. Since conditions (1) and (2) will provide 1 equation each, C would most likely be the answer.

Recall 3- Principles and Choose C as the most likely answer. Let’s look at both conditions combined together.

Condition (1) tells us that x is a multiple of 3.

=> x = 3m - where m is an integer

Condition (2) tells us that y is a multiple of x.

=> y = xp - where p is an integer

From them, we cannot determine whether xy is a multiple of 12.

For example, if x = 6 and y = 12, then y = 12 = 2*6 = 2x (y is a multiple of x) and we get xy = 6*12, which is a multiple of 12, so we get yes as an answer.

However, if x = y = 9, then y = 9 = 1 * 9 = x (y is a multiple of x) and we get xy = 9 * 9 = 81, which is not a multiple of 12, so we get no as an answer.

The answer is not a unique YES or a NO; both conditions combined are not sufficient according to Common Mistake Type 1 which states that the answer should be a unique YES or a NO.

Both conditions together are not sufficient.

Therefore, E is the correct answer.

Answer: E
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 16 Jul 2021, 09:55
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Que: Is xy < 15?

(1) x < 4 and y < 2
(2) x < −4 and y < −3
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 17 Jul 2021, 22:09
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Que: Is xy < 15?

(1) x < 4 and y < 2
(2) x < −4 and y < −3
Show more


Solution: To save time and improve accuracy on DS questions in GMAT, learn and apply the Variable Approach.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Visit https://www.mathrevolution.com/gmat/lesson for details.

Now we will solve this DS question using the Variable Approach.

Let’s apply the 3 steps suggested previously.

Follow the first step of the Variable Approach by modifying and rechecking the original condition and the question.

We have to find whether xy < 15.

Follow the second and the third step: From the original condition, we have 2 variables (x and y). To match the number of variables with the number of equations, we need 2 equations. Since conditions (1) and (2) will provide 1 equation each, C would most likely be the answer.

Recall 3- Principles and Choose C as the most likely answer. Let’s look at both conditions combined together.

Condition (1) tells us that x < 4 and y < 2.

Condition (2) tells us that x < −4 and y < −3.

From them, we can determine whether xy<15.

For example, If x = -10 and y = -4.

=> xy = (-10)(-4) = 40 > 15 – Is xy < 15 - NO

If x = -4.1 and y = -3.1.

=> xy = (-4.1)(-3.1) = 12.71 < 15 – Is xy < 15 - YES

The answer is not a unique YES or a NO; both conditions combined are not sufficient according to Common Mistake Type 1 which states that the answer should be a unique YES or a NO.

Both conditions together are not sufficient.

Therefore, E is the correct answer.

Answer: E
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 17 Jul 2021, 22:22
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Que: What is the value of x?

1. \(3(x + y) = x + 3y\).
2. \(x^2 + y^2 = (x + y)^2\).
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 19 Jul 2021, 02:11
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Que: What is the value of x?

1. \(3(x + y) = x + 3y\).
2. \(x^2 + y^2 = (x + y)^2\).
Show more


Solution: To save time and improve accuracy on DS questions in GMAT, learn and apply the Variable Approach.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Visit https://www.mathrevolution.com/gmat/lesson for details.

Now we will solve this DS question using the Variable Approach.

Let’s apply the 3 steps suggested previously.

Follow the first step of the Variable Approach by modifying and rechecking the original condition and the question.

We have to find the value of x.

Follow the second and the third step: From the original condition, we have 1 variable (x). To match the number of variables with the number of equations, we need 1 equation. Since conditions (1) and (2) will provide 1 equation each, D would most likely be the answer.

Recall 3- Principles and Choose D as the most likely answer. Let’s look at each condition separately.

Condition (1) tells us that \(3(x + y) = x + 3y\).

=> 3x + 3y = x + 3y

=> 3x - x = 0

=> x = 0

The answer is unique and condition (1) alone is sufficient according to Common Mistake Type 2 which states that the answer should be unique.

Condition (2) tells us that \(x^2 + y^2 = (x + y)^2\).

=> \(x^2 + y^2 = (x + y)^2\)

=> \(x^2 + y^2 = x^2 + y^2 + 2xy\)

=> 2xy = 0

=> xy = 0

We don’t have a value of ‘y’ and hence we cannot find the value of ‘x’.

The answer is not unique and condition (2) alone is not sufficient according to Common Mistake Type 2 which states that the answer should be unique.

Condition (1) alone is sufficient.

Therefore, A is the correct answer.

Answer: A
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 19 Jul 2021, 02:19
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Que: If P, Q, & R are numbers on the number line, not necessarily in that order, is |P − R| ≥ 18?

(1) |P − Q| = 80.
(2) |Q − R| = 90.
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