Math Revolution DS Expert - Ask Me Anything about GMAT DS

Que: What is the total number of golf clubs that Paul and Mike have?

(1) Paul has 60 percent more golf clubs than Mike.
(2) Mike has between 9 and 14 golf clubs.

Que: If x is an integer, is \(x^3 - x\) a multiple of 12?

(1) x- 1 is an even integer.
(2) x is an odd integer.

Solution: To save time and improve accuracy on DS question in GMAT, learn and apply 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 ‘Is \(x^3 - x\) a multiple of 12’- where ‘x’ is an integer

Modify the question:

=> \(x^3 - x\) = 12p? – where ‘p’ is an integer

=> x(\(x^2 - 1\)) = 12p?

=> x (x-1) (x+1) = 12p?

=> (x-1) x (x+1) = 12p?

=> (x-1) x (x+1) = 4q? (since x-1, x, x+1 are consecutive integers and their product must be a multiple of 3.

So, we have to find whether x-1 = even or x = odd?

Condition (1) tells us that x-1 is an even integer

=> Is x-1 = even - YES

The answer is unique, so the condition (1) alone is sufficient, according to CMT 1 - there must be a unique YES or a NO.

Condition (2) tells us that x is an odd integer

=> Is x = odd - YES

The answer is unique, so condition (2) alone is sufficient, according to CMT 1 - there must be a unique YES or a NO.

** Tip 1: When condition (1) = condition (2) then 95% likely that answer is D

Each condition alone is sufficient.

Therefore, D is the correct answer.

Answer: D

Solution: To save time and improve accuracy on DS question in GMAT, learn and apply 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 total number of golf clubs that Paul and Mike have

Let us assign a variable: Suppose Paul has p golf clubs and Mike has m golf clubs.

Follow the second and the third step: From the original condition, we have 2 variables (p and m). 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 Paul has 60 percent more golf clubs than Mike and Condition (2) tells us that Mike has between 10 and 15 golf clubs.

=> Converting into equation: p = m + 60%m = 1.6m and 9< m < 14

=> Since m is an integer => m must be 10,11,12,or 13

However,

If m = 10 => p = 1.6m => 1.6 * 10 => 16 can be the number of golf clubs that Paul has (∵ It’s an integer)

If m = 11 => p = 1.6m => 1.6 * 11 => 17.6 cannot be the number of golf clubs that Paul has (∵ It’s a decimal number)

If m = 12 => p = 1.6m =>1.6 * 12 => 19.2 cannot be the number of golf clubs that Paul has (∵ It’s a decimal number)

If m = 13 => p = 1.6m =>1.6 * 13 => 20.8 cannot be the number of golf clubs that Paul has (∵ It’s a decimal number)

=> ∴ Paul has 16 golf clubs and Mike has 10 golf clubs

=> Total number of golf clubs possessed by Paul and Mike: 16 + 10 = 26

The answer is unique, so the conditions combined are sufficient, according to CMT 2 - there must be only one answer.

Both conditions together are sufficient.

Therefore, C is the correct answer.

Answer: C

Que: Machine A and machine B produce toys at their constant rates, respectively. In how many hours does machine A produce the total number of toys?

(1) Machine B produces 500 toys in 5 hours.
(2) The total number of toys that machine A must produce is 1,500.

Que: If the ratio of the numbers of men to women to children in a certain room is 5 to 3 to 7, how many people are in the room?

(1) The total number of men and women in the room is 8.
(2) The number of children in the room is between 6 and 8.

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 \(t_1\) =>(2 machines: \(r_1* t_1 = w_1\) and \(r_2 * t_2 = w_2\))

Follow the second and the third step: From the original condition, we have 6 variables (\(r_1, t_1, w_1, r_2, t_2,\)and \(w_2\)) and 2 Equations (\(r_1* t_1 = w_1\) and \(r_2 * t_2 = w_2\)). To match the number of variables with the number of equations, we need 4 more 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 each condition separately.

Condition (1) tells us that Machine B produces 500 toys in 5 hours => \(r_2 *5 = 500\) => \(r_2= 100\)

Condition (2) tells us that the total number of toys that machine A must produce is 1,500 => \(r_1\) * \(t_1\) = \(w_1\)= 1,500

Thus, the Work rate of Machine A is unknown => Cannot determine the unique value of \(t_1\).

The answer is not unique, so the conditions combined are not sufficient, according to CMT 2 - there must be one answer.


Both conditions together are not sufficient.

Therefore, E is the correct answer.

Answer: E

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.

Let us assign the variable: men (m) ; women(w) ; children(c)

Given: m = 5k ; w = 3k ; c = 7k – where ‘k’ is a positive integer

We have to find the total number of people in the room => 5k + 3k + 7k = 15k – We have to find the value of ‘15k’

Follow the second and the third step: From the original condition, we have 4 variables (m, w, c, and k) and 3 equations (m = 5k; w = 3k; c = 7k). 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 separately.

Condition (1) tells us that the total number of men and women in the room is 11

=> 5k + 3k = 8
=> 8k = 8
=> k = 1

Therefore, 15k = 15 * 1 = 15

The answer is unique, so condition (1) alone is sufficient, according to CMT 2 - there must be only one answer

Condition (2) tells us that the number of children in the room is between 6 and 8

=> 6 < 7k < 8
=> 7k = 7
=> k = 1

Therefore, 15k = 15 * 1 = 15.

The answer is unique, so condition (2) alone is sufficient, according to CMT 2 - there must be only one answer

** Tip 1: When condition (1) = condition (2) => 95% likely that answer is D

Each condition alone is sufficient.

Therefore, D is the correct answer.

Answer: D

Que: If a certain machine produces toys at a constant rate, how many minutes will it take the machine to produce 1,200 toys?

(1) It takes the machine 75 minutes to produce 40 toys.
(2) It takes the machine 2.25 minutes to produce 2 toys.

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.

DS question dealing with the work rate of one machine => rt = w

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 t – 1 machine rt = 1,200

Follow the second and the third step: From the original condition, we have 2 variables (r and t) and 1 equation (rt = 1,200). 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 separately.

\(Condition (1) tells us that it takes the machine 75 minutes to produce 40 toys.\)

=> rt = w

=> r * 75 minutes = 40

=> Multiply by 30 on both sides

=> r * 75 minutes * 30 = 40 * 30

=> r * 1,350 minutes = 1,200

=> Machine makes 1,200 toys in 1,350 minutes

=> t = 1,350


The answer is unique, so condition (1) alone is sufficient, according to CMT 2 - there must be only one answer

Condition (2) tells us that it takes the machine 2.25 minutes to produce 2 toys.

=> rt = w

=> r * 2.25 minutes = 2

=> Multiply by 600 on both sides

=> r * 2.25 minutes * 600 = 2 * 600

=> r * 1,350 minutes = 1,200

=> Machine makes 1,200 toys in 1,350 minutes

=> t = 1,350

The answer is unique, so condition (2) alone is sufficient, according to CMT 2 - there must be one answer.

** Tip 1: When condition (1) = condition (2) => 95% likely that answer is D

Each condition alone is sufficient.

Therefore, D is the correct answer.

Answer: D

Que : When the equation \(x ^2 + ax + b = 0\) has roots p and q, what is the value of p + q?

(1) a = 4
(2) b = 9

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 + q.

=> Given: \(x ^2 + ax + b = 0\) has ‘p’ and ‘q’ as its roots.

=> (x – p) (x – q)=0 => \(x^ 2 – (p + q)x + pq = 0\)

=> a=-(p+q) and b=pq

=> We have to find the value of a

Condition (1) tells us that a = 4.

=> a = 4 = -(p + q)

=> -( p + q) = 4

=> p + q = -4

The answer is unique, so condition (1) alone is sufficient, according to CMT 2 - there must be only one answer

Condition (2) tells us that it b = 9.

=> b = pq = 9

=> If p = q = 3, then pq = 3 * 3 = 9 => p + q = 3 + 3 = 6

=> But if p =1; q = 9, then pq = 1 * 9 = 9 => p + q = 1 + 9 = 10

The answer is not unique, so condition (1) alone is not sufficient, according to CMT 2 - there must be only one answer.

Condition (1) alone is sufficient.

Therefore, A is the correct answer.

Answer: A

Que: \((3^{a + b} )(3^{a - 2b})\) = ?

(1) a = 3.
(2) 2a – b = 5.

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.

First of the seven properties of exponents: \(a^m * a^n = a^ {m + n}\)

Multiplication of the same base numbers with the same or different exponents = Addition of the exponents

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 \((3^{a + b} )(3^{a - 2b})\)

First property of exponents: \((3^{a + b} )(3^{a - 2b}) = 3^{a + b + a – 2b} = 3^ {2a – b}\)

We have to find the value of 2a - b

Condition (2) tells us that 2a – b = 5

=> \(3^ {2a – b} = 3^5 = 243\)

The answer is unique, so condition (2) alone is sufficient, according to CMT 2 - there must be one answer.

Condition (1) tells us that a = 3

=> Cannot determine the unique value of 2a – b

The answer is not unique, so condition (1) alone is not sufficient, according to CMT 2 - there must be one answer.

Condition (2) alone is sufficient.

Therefore, B is the correct answer.

Answer: B

Que: If x and y are integers, is x + y an even number?

(1) x + 4y = odd.
(2) 3x + 11y = even.

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]

Let’s follow the first step of the Variable Approach by modifying and rechecking the original condition and the question.

We have to find whether x+y = even – where ‘x’ and ‘y’ are integers, in order to be x + y = even, (x,y) should be (even, even) or (odd, odd).

Thus, let look at condition (2), it tells us that 3x + 11y = even, from which we get (x,y) = (even , even) since 3*even + 11*even = even + even = even, or (x,y) = (odd, odd) since 3*odd + 11*odd = odd + odd = even. So, the answer becomes yes.

The answer is unique YES, so the conditions combined are sufficient, according to CMT 1 - there must be a unique YES or a NO.

Condition (1) Condition (1) tells us that x + 4y = odd

=> x = odd [∵ 4y=even]

=> x = y = odd => x + y = odd + odd = even => Is x + y = even => YES

=> x = odd ; y = even => x + y = odd + even = odd => Is x + y = even => NO

The answer is not a unique Yes or a NO, so the condition (1) alone is not sufficient, according to CMT 1 - there must be a unique YES or a NO.

Condition (2) alone is sufficient.

Therefore, B is the correct answer.

Answer: B

Que: Is an integer 'n' odd?

(1) \(n – 5\) is an even integer.

(2) \(\frac{n}{5}\) is an odd integer.