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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 [?]: 17027 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17027 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17027 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17027 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
MathRevolution wrote:
Que: If |x + 3| = 2, what is the value of x?

(1) x < 0
(2) $$x^2 + 6x + 5 = 0$$

Solution: To save time and improve accuracy on DS questions 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. [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 + 3| = 2.

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

=> If x + 3 = 2, then x = 2 – 3 = -1

=> But if x + 3 = -2, then x = -2 – 3 = -5

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

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.

Both values of x = -1 and – 5 are less than zero. So, we don’t have a unique value of ‘x’

The answer is not a unique value; 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 $$x^2 + 6x + 5 = 0$$

=> $$x^2 + 6x + 5 = 0$$

=> (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.

Both values of x = -1 and – 5 are less than zero. So, we don’t have a unique value of ‘x’

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

Both conditions combined are not sufficient.

Therefore, E is the correct answer.

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17027 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Que: If x and y are positive integers, what is the value of x?

(1) $$3^x + 5^y = 134$$.
(2) y = 3
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17027 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
MathRevolution wrote:
Que: If x and y are positive integers, what is the value of x?

(1) $$3^x + 5^y = 134$$.
(2) y = 3

Solution: To save time and improve accuracy on DS questions 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 value of ‘x – where ‘x’ and ‘y’ are positive integers.

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 $$3^x + 5^y = 134$$

Condition (2) tells us that y = 3

=> $$3^x + 5^3 = 134$$

=> $$3^x + 125 = 134$$

=> $$3^x = 134 - 125 = 9$$

=> $$3^x = 3^2$$

Therefore, x = 2

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.

Condition (1) tells us that $$3^x + 5^y = 134$$

Since the exponents of 5 would reach 134 faster than the exponents of 3, we need to try with the exponents of 5 so that we can get the answer(s) in the least possible trials.

If y = 1, then

=> $$3^x + 5^1 = 134$$

=> $$3^x + 5 = 134$$

=> 3x = 134 - 5 = 129 [129 cannot be expressed as an exponent of 3, so y ≠ 1]

If y = 2, then

=> $$3^x + 5^2 = 134$$

=> $$3^x + 25 = 134$$

=> $$3^x = 134 - 25 = 109$$ [109 cannot be expressed as an exponent of 3, so y ≠ 2]

But if y = 3, then

=> $$3^x + 5^3 = 134$$

=> $$3^x + 125 = 134$$

=> $$3^x = 134 - 125 = 9$$ [9 can be expressed as an exponent of 3, so y = 2]

=> $$3^x = 3^2$$

Therefore, x = 2

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 y = 3

=> But ‘x’ 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.

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17027 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Que: If x and y are positive integers, is xy a multiple of 18?

(1) x is a multiple of 9.
(2) y is a multiple of x.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17027 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
MathRevolution wrote:
Que: If x and y are positive integers, is xy a multiple of 18?

(1) x is a multiple of 9.
(2) y is a multiple of x.

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 whether xy is a multiple of 18 – where ‘x’ and ‘y’ are positive integers.

=> xy = 18n – 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 9

=> x = 9m ; where m is any integer

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

=> y = xp ; where p is any integer

From them, we cannot determine whether xy is a multiple of 18.

For example, if x=9 and y=18, then y=18=2*9=2x (y is a multiple of x) and we get xy=9*18, which is a multiple of 18, 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 18, 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 combined are not sufficient.

Therefore, E is the correct answer.

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17027 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Que: Is xy < 10?

(1) x < 5 and y < 2
(2) x < −3 and y < −1
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17027 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
MathRevolution wrote:
Que: Is xy < 10?

(1) x < 5 and y < 2
(2) x < −3 and y < −1

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 whether xy < 10.

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 < 5 and y < 2

Condition (2) tells us that x < −3 and y < −1

From them, we cannot determine whether xy<10. For example, If x = -8 and y = -6.

=> xy = (-8)(-6) = 48 > 10 – Is xy < 10 - NO

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

=> xy = (-4)(-2) = 8 < 10 – Is xy < 10 - YES

The answer is not a unique YES or a NO; both conditions combined together 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 [?]: 17027 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Que: What is the value of x?

1. $$2(x + y) = x + 2y$$
2. $$x^3 + y^3 = (x + y)^3$$
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17027 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
MathRevolution wrote:
Que: What is the value of x?

1. $$2(x + y) = x + 2y$$
2. $$x^3 + y^3 = (x + y)^3$$

Solution: To save time and improve accuracy on DS questions 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 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 $$2(x + y) = x + 2y$$

=> 2x + 2y = x + 2y

=> 2x - 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 $$x^3 + y^3 = (x + y)^3$$

=> $$x^3 + y^3 = (x + y)^3$$

=> $$x^3 + y^3 = x^3 + y^3 + 3x^2y + 3xy^2$$

=> $$3x^2y + 3xy^2 = 0$$

=> $$x^2y + xy^2 = 0$$

=> $$xy( x + y) = 0$$

We don’t have the 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.

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17027 [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 4?

(1) n is an odd integer.
(2) n(n+1) is divisible by 6.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17027 [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 4?

(1) n is an odd integer.
(2) n(n+1) is divisible by 6.

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 whether n (n − 1) (n + 1) is divisible by 4, which means that we have to find whether n is odd since (n-1), n, (n+1) are 3 consecutive integers,

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

=> Say n = 2k + 1; where k is an integer.

=> n(n-1)(n+1) = (2k + 1) (2k) (2k + 2

=> 4k (2k + 1) (k + 1)

Hence, n (n − 1) (n + 1) divisible by 4 - Yes

The answer is a 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 6, from which we cannot determine whether n=odd. For example,

If n = 3

=> (3) ( 3 + 1) = 3 * 4 = 12 is divisible by 6 , and n (n − 1) (n + 1) = 3 * 2 * 4 = 24 is divisible by 4 - YES

If n = 2

=> (2) ( 2 + 1) = 2 * 3 = 6 is divisible by 6, however n (n − 1) (n + 1) = 2 * 1 * 3 = 6 is not divisible by 4 - NO

The answer is not unique, YES or No, and 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 (1) alone is sufficient.

Therefore, A is the correct answer.

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17027 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Que: If a, b, and c are integers, is (a − b − c) odd?

(1) a and b are even and c is odd.
(2) a, b and c are consecutive integers.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17027 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
MathRevolution wrote:
Que: If a, b, and c are integers, is (a − b − c) odd?

(1) a and b are even and c is odd.
(2) a, b and c are consecutive integers.

Solution: To save time and improve accuracy on DS questions 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. [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 a – b – c is odd’ – where a, b, and c are integers.

For a - b - c = odd, (a,b,c) = (even,odd,even), (even,even,odd), or (odd, even, even).

Thus, look at condition (1), it tells us that 'a' and 'b' are 'even' and 'c' is 'odd', from which a - b - c = even - even - odd = odd.

So we get YES as an answer. The answer is unique, yes, so 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 a, b and c are consecutive integers, from which we cannot determine whether a - b - c = odd.

For example, if (a,b,c) = (2,3,4), then a - b - c = 2 - 3 - 4 = -5 = odd we get YES as answer.

However if (a,b,c) = (1,2,3), then a - b - c = 1 - 2 - 3 = -4 = even we get NO as answer.

The answer is not unique, both yes and no, so 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 (1) alone is sufficient.

Therefore, A is the correct answer.

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17027 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Que: If m, n, and p are positive integers and 4m + 5n = p, does p and 10 have a common factor other than 1?

(1) m is a multiple of 5.
(2) n is a multiple of 5.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17027 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
MathRevolution wrote:
Que: If m, n, and p are positive integers and 4m + 5n = p, does p and 10 have a common factor other than 1?

(1) m is a multiple of 5.
(2) n is a multiple of 5.

Solution: To save time and improve accuracy on DS questions 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 verify whether 'p' and '10' have a common factor other than 1 – where ‘m’, ‘n’, and ‘p’ are positive integers and 4m + 5n = p.

For 'p' and '10' to have a common factor other than 1, since 5n is a multiple of 5, 4m should be divisible by 5 or m should be divisible by 5.

Thus, look at condition (1), it tells us that m is a multiple of 5.

Assume m=5t where 't' is an integer, we get

=> 4m + 5n = 4(5t) + 5n = 5(4t + n) = p, so p has a factor of 5.

Thus, p and 10 have a common factor other than 1, which is equal to 5, so we get YES as an answer.

The answer is unique, yes, so 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 is a multiple of 5, from which we cannot determine whether p and 10 have a common factor other than 1.

For example, if n=5 and m=5, then p = 4m + 5n = 4(5) + 5(5) = 45.

And 'p' and '10' have a common factor other than 1, which is equal to 45 and we get YES as an answer.

However, if n=5 and m=1, then p = 4m + 5n = 4(1) + 5(5) = 29. And p and 10 have not a common factor other than 1, which is equal to 1 and we get NO as an answer.

The answer is not unique, YES or NO, so 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 not sufficient.

Therefore, A is the correct answer.

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17027 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Que: For a positive integer x, what is the value of the hundreds digit of $$30^x$$?

(1) x ≥ 3.

(2) $$\frac{x}{ 3}$$ is an integer.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17027 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
MathRevolution wrote:
Que: For a positive integer x, what is the value of the hundreds digit of $$30^x$$?

(1) x ≥ 3.

(2) $$\frac{x}{ 3}$$ is an integer.

Solution: To save time and improve accuracy on DS questions 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 value of the hundreds digit of $$30^x$$ - where ‘x’ is a positive integer

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.

Condition (1) tells us that x ≥ 3

Since x ≥ 3, the number of trailing zeroes in $$30^x$$ must be at least ‘three.’

For example,

=> For x = 3, $$30^x$$ = $$30^3$$ = 27,000

=> For x = 4, $$30^x$$ = $$30^4$$ = 810,000

Thus, the hundreds digit of $$30^x$$ is ‘0’.

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 $$\frac{x }{3}$$ is an integer.

Thus, the possible values of x are 3, 6, 9 . . .

=> For x = 3, $$30^x$$ = $$30^3$$ = 27,000

=> For x = 6, $$30^x$$ = $$30^6$$ = 729,000,000

Thus, the hundreds digit of $$30^x$$ is ‘0’.

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

Also, according to Tip 1, it is about 95% likely that D is the answer when condition (1) = condition (2).

Each condition alone is sufficient.

Therefore, D is the correct answer.