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# Math Revolution DS Expert - Ask Me Anything about GMAT DS

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17044 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17044 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17044 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17044 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Que: Sequence S is such that the difference between a term and its previous term is constant and has 150 terms. What is the 100th term of sequence S?

(1) The 50th term of Sequence S is 105.
(2) The 90th term of Sequence S is −50.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17044 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Que: If |x - 2| = 3, what is the value of x?

(1) $$x > 0$$
(2) $$x^2 - 4x - 5 = 0$$
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17044 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
MathRevolution wrote:
Que: Sequence S is such that the difference between a term and its previous term is constant and has 150 terms. What is the 100th term of sequence S?

(1) The 50th term of Sequence S is 105.
(2) The 90th term of Sequence S is −50.

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.

Sequence S has the difference between a term and its previous term constant. Thus, it is an arithmetic sequence.

The general term of an arithmetic sequence Tn = a + (n-1)d – where ‘a’ is the first term, n is total terms and d is a common difference.

We have n = 150. Thus, $$T_{150} = a + (150 - 1)d = a + 149d$$.

We have to find n = 100 or a + 99d.

Follow the second and the third step: From the original condition, we have 2 variables (‘a’ and d). 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 the 50th term of Sequence S is 150: 150 = a +49d – Equation (1)

Condition (2) tells us that the 90th term of Sequence S is −50: -50 = a + 89d – Equation (2)

Equation (1) – Equation (2)

=> 150 – (- 50) = a + 49d – ( a - 99d)

=> 200 = - 50d

=> d = -4

Substituting d = 4 into equation (1):

=> 150 = a + 49(-4)

=> 150 = a - 196

=> 150 + 196 = a

=> a = 346

Therefore, 100th term a + 99d = 346 + 99(-4) = - 50

The answer is a unique value; both 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.

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17044 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
MathRevolution wrote:
Que: If |x - 2| = 3, what is the value of x?

(1) $$x > 0$$
(2) $$x^2 - 4x - 5 = 0$$

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 - 2| = 3.

Since, |x - 2| = 3, then x - 2 = 3 or -3.

=> If x - 2 = 3, then x = 3 + 2 = 5

=> But if x - 2 = -3, then x = -3 + 2 = -1

We have to find if x = 5 or -1.

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 the condition (1) that tells us that x > 0.

Out of both values of x = 5 and – 1, x= 5 is greater than zero. So, we have a unique value of ‘x’

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 $$x^2 - 4x - 5 = 0$$

=> $$x^2 - 4x - 5 = 0$$

=> (x + 1) (x - 5) = 0

=> x = -1 or 5

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.

Condition (1) alone is sufficient.

Therefore, A is the correct answer.

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17044 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Que: Is xy < 18?

(1) x < 6 and y < 3
(2) x < −4 and y < −2
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17044 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Que: If n is a positive integer, is n (n − 1) (n + 1) divisible by 8?

(1) n is an odd integer.
(2) n(n+1) is divisible by 7.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17044 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
MathRevolution wrote:
Que: Is xy < 18?

(1) x < 6 and y < 3
(2) x < −4 and y < −2

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 < 18.

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 < 6 and y < 3.

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

From them, we cannot determine whether xy < 18.

For example, If x = -8 and y = -6.

=> xy = (-8)(-6) = 48 > 18 – Is xy < 18 - NO

But if x = -4 and y = -2.

=> xy = (-4)(-2) = 8 < 18 – Is xy < 18 - 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.

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17044 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
MathRevolution wrote:
Que: If n is a positive integer, is n (n − 1) (n + 1) divisible by 8?

(1) n is an odd integer.
(2) n(n+1) is divisible by 7.

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 n (n − 1) (n + 1) is divisible by 8, which means that we have to find whether n is odd since (n-1), n, (n+1) are 3 consecutive integers, or n is even.

Thus, let’s look at condition (1), which tells us that ‘n’ is an odd integer.

=> If n = 5

=> n(n-1)(n+1) = 5 * 4 * 6 = 120

Hence, n (n − 1) (n + 1) divisible by 8 - Yes

=> If n = 3

=> n(n-1)(n+1) = 3 * 2 * 4 = 24

Hence, n (n − 1) (n + 1) divisible by 8 - Yes

The answer is unique YES and condition (1) alone is 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 n(n+1) is divisible by 7, from which we cannot determine whether n=odd. For example,

If n = 7

=> (7) ( 7 + 1) = 7 * 8 = 56 is divisible by 7 , and n (n − 1) (n + 1) = 7 * 6 * 8 is divisible by 8 - YES

If n = 6

=> (6) (6 + 1) = 6 * 7 = 42 is divisible by 7, however n (n − 1) (n + 1) = 6 * 5 * 7 = 210 is not divisible by 8 - NO

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

Condition (1) alone is sufficient.

Therefore, A is the correct answer.

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17044 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Que: If A, B, & C are numbers on the number line, not necessarily in that order, is |A − C| ≥ 10?

(1) |A − B| = 60
(2) |B − C| = 50
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17044 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
MathRevolution wrote:
Que: If A, B, & C are numbers on the number line, not necessarily in that order, is |A − C| ≥ 10?

(1) |A − B| = 60
(2) |B − C| = 50

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 is |A − C| ≥ 10.

Follow the second and the third step: From the original condition, we have 3 variables (P, Q, and R). To match the number of variables with the number of equations, we need 3 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 |A − B| = 60 => A – B = ± 60

Condition (2) tells us that |B − C| = 50 => B – C = ± 50

=> A – B + B – C = ± 60 ± 50

=> 60 + 50 = 110 OR 60 – 50 = 10 OR -60 + 50 = -10 OR -60-50 = -110

=> A – C = ± 110 OR ± 10

=> |A − C| = 110 OR 10

=> Is |A − C| ≥ 10 – YES

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

Both conditions combined together are sufficient.

Therefore, C is the correct answer.

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17044 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Que: Is 20% of n greater than 30% of the sum of n and $$\frac{1}{4}$$?

(1) 0 < n < 2.
(2) n > 0.25.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17044 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
MathRevolution wrote:
Que: Is 20% of n greater than 30% of the sum of n and $$\frac{1}{4}$$?

(1) 0 < n < 2.
(2) n > 0.25.

Solution: Forget the conventional way to solve DS questions.We will solve this DS question using the variable approach.

The first step of the Variable Approach: The first step and the priority is to modify and recheck the original condition and the question to suit the type of information given in the condition.

To master the Variable Approach, visit https://www.mathrevolution.com and check our lessons and proven techniques to score high in DS questions.

Learn the 3 steps. [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 ‘Is 20% of n greater than 30% of the sum of n and $$\frac{1}{ 4}$$’?

=> 20% of n > 30% of (n +$$\frac{1}{4}$$)

=> $$\frac{20}{100}$$ * n > $$\frac{30}{100}$$ * (n + $$\frac{1}{4}$$)

=> $$\frac{20n}{100} > \frac{30n}{100} + \frac{30}{100} * 4$$

=> $$\frac{n}{5} > \frac{3n}{10} + \frac{6}{5}$$

=> $$\frac{-6}{5} > \frac{3n}{10} - \frac{n}{5}$$

=> $$\frac{-6}{5} > \frac{(3n – 2n) }{ 10 }$$

=> $$\frac{-6}{5} > \frac{n }{ 10}$$

=> -12 > n

=> n < -12

We have to know ‘Is n < -12’?

Condition (1) tells us that 0 < n < 2.

=> n < -12

Since the answer is a unique NO, condition (1) alone is sufficient by CMT 1 which states that there should be a unique Yes or a NO.

Condition (2) tells us that n > 0.25.

=> n < -12

Since the answer is a unique NO, condition (1) alone is sufficient by CMT 1 which states that there should be a unique Yes or a NO.

Each condition alone is sufficient.

So, D is the correct answer.

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17044 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Que: If xy = 8, is x > y?

(1) y ≥ 4
(2) y ≤ 4
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17044 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
MathRevolution wrote:
Que: If xy = 8, is x > y?

(1) y ≥ 4
(2) y ≤ 4

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’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 ‘Is x > y’? - where 'xy = 8'

Second and the third step of Variable Approach: From the original condition, we have 2 variables (x, and y) and 1 Equation (xy = 8). 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 both conditions together.

Let’s take a look at each condition.

Condition (1) tells us that y ≥ 4.

If $$y = \frac{8}{x}$$ into y ≥ 4, then we get $$\frac{8}{x} ≥ 4$$.

Also y ≥ 4 > 0 and xy = 8 > 0, so we get x > 0 and if we multiply both sides of $$\frac{8}{x} ≥ 4$$ by x, we get 8 ≥ 4x and divide by 4, we get 2 ≥ x.

And since y ≥ 4 > 2 ≥ x, we get y > x . Therefore, NO becomes an answer.

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

Condition (2) tells us that y ≤ 4.

=> If y = 2, then x * 2 = 8 => x = 4 => x > y - YES

=> If y = 3, then x * 3 = 8 => x = 2.xx => x > y - NO

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

Condition (1) alone is sufficient.

Therefore, A is the correct answer.

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17044 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Que: How many more girls than boys are in the class?

(1) Twice the boys subtracted from girls are 15.
(2) The number of girls in the class equals the square of the number of boys in the class.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17044 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
MathRevolution wrote:
Que: How many more girls than boys are in the class?

(1) Twice the boys subtracted from girls are 15.
(2) The number of girls in the class equals the square of the number of boys in the class.

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 variables: Boys (b) and Girls (g)

We have to find the value of g – b.

Follow the second and the third step: From the original condition, we have 2 variables (b and g). 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 twice the boys subtracted from girls are => g - 2b = 15

Condition (2) tells us that the number of girls in the class equals the square of the number of boys in the class => $$g = b^2$$

=> $$g -2b = 15$$

=> $$b^2 - 2b – 15=0$$

=> $$b^2 – 5b + 3b – 15 = 0$$

=> (b - 5) (b + 3) = 0

=> b = 5, -3 [-3 not possible]

Therefore $$b = 5$$ and $$g = b^2 => g = (5)^2 => g = 25$$

=> g – b = 25 – 5 = 20

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

Both conditions combined together are sufficient.

Therefore, C is the correct answer.

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17044 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
(1) $$\frac{q}{p} = \frac{2}{3}$$.
(2) $$q> 0$$ and $$p > 0.$$