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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: 8456
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

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21 Nov 2018, 03:36
MathRevolution wrote:
[Math Revolution GMAT math practice question]

(number property) If $$n$$ is an integer between $$30$$ and $$50$$ inclusive, what is the value of $$n$$?

1) When $$n$$ is divided by $$8$$, the remainder is $$7$$
2) When $$n$$ is divided by $$16$$, the remainder is $$7$$

=>

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.

Since we have $$1$$ variable (n) and $$0$$ equations, D is most likely to be the answer. So, we should consider each condition on its own first.

Condition 1)
We can express $$n = 8k+7$$ for some integer $$k$$.
If $$k = 3$$, then $$n = 31.$$
If $$k = 4$$, then $$n = 39.$$
Since we don’t have a unique solution, condition 1) is not sufficient.

Condition 2)
We can express $$n = 16m+7$$ for some integer $$m$$.
If $$m = 2$$, then $$n = 39.$$
If $$m = 1$$, then $$n = 23$$ and $$n < 30.$$
If $$m = 3,$$ then $$n = 55$$ and $$n > 50.$$
Thus $$n = 39$$ is the unique solution and condition 2) is sufficient.

Therefore, B is the answer.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8456 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 21 Nov 2018, 03:36 [Math Revolution GMAT math practice question] (number property) If $$n$$ is an integer greater than $$1$$, what is the value of $$n$$? 1) $$n$$ is a prime number 2) $$\frac{(n+2)}{n}$$ is an integer _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8456
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

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22 Nov 2018, 02:13
MathRevolution wrote:
[Math Revolution GMAT math practice question]

(number property) If $$p, q$$ and $$r$$ are prime, with $$p<q<r, p=?$$

$$1) (pq)^3=216$$
$$2) (pr)^3=1000$$

=>

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.

Since we have $$3$$ variables ($$p, q$$ and $$r$$) and $$0$$ equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)

$$(pq)^3=216$$
$$=> p^3q^3=2^33^3$$
$$=> p = 2$$ and $$q = 3$$, since $$p$$ and $$q$$ are prime numbers with $$p < q.$$

$$(pr)^3=1000$$
$$=> p^3r^3=2^35^3$$
$$=> p = 2$$ and $$r = 5$$, since $$p$$ and $$r$$ are prime numbers with $$p < r.$$

While we have checked both conditions together, we have shown that conditions 1) and 2) are equivalent to each other in terms of $$p$$. So, each condition is sufficient by Tip 1).
FYI, Tip 1) of the VA method states that D is most likely to be the answer if conditions 1) and 2) provide the same information.

Therefore, the answer is D.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8456 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 22 Nov 2018, 02:14 [Math Revolution GMAT math practice question] (inequality) If $$x$$ and $$y$$ are positive, is $$1<x<y$$? $$1) √x<x<y$$ $$2) 1<√x<y$$ _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8456
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

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23 Nov 2018, 00:50
MathRevolution wrote:
[Math Revolution GMAT math practice question]

(number property) If $$n$$ is an integer greater than $$1$$, what is the value of $$n$$?

1) $$n$$ is a prime number
2) $$\frac{(n+2)}{n}$$ is an integer

=>

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.

Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
Since there are many prime numbers, condition 1) is not sufficient.

Condition 2)
If $$n = 1$$, then $$\frac{(n+2)}{n} = 3$$ is an integer.
If $$n = 2,$$ then $$\frac{(n+2)}{n} = 2$$ is an integer.
Since we don’t have a unique solution, condition 2) is not sufficient.

Conditions 1) & 2)
If $$n = 2$$, then $$\frac{(n+2)}{n} = 2$$ is an integer.
If $$n = 3$$, then $$\frac{(n+2)}{n} = \frac{5}{2}$$ is not integer.
If $$n$$ is a prime number bigger than $$2$$, $$\frac{(n+2)}{n}$$ is not an integer.
Thus $$n = 2$$ is the unique solution and both conditions together are sufficient.

Therefore, C is the answer.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8456 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 23 Nov 2018, 00:51 [Math Revolution GMAT math practice question] (inequality) Is $$x^3-4x>0？$$ $$1) x>2$$ $$2) x>-2$$ _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8456
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

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25 Nov 2018, 18:34
MathRevolution wrote:
[Math Revolution GMAT math practice question]

(inequality) If $$x$$ and $$y$$ are positive, is $$1<x<y$$?

$$1) √x<x<y$$
$$2) 1<√x<y$$

=>

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.

Since we have $$2$$ variables ($$x$$ and $$y$$) and $$0$$ equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
Since $$\sqrt{x}<x<y$$ and $$1<\sqrt{x}<y$$, we have $$1<\sqrt{x}<x<y.$$ Both conditions together are sufficient.

Since this question is an inequality question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
Since $$\sqrt{x}<x,$$ we have $$x > 1.$$
Thus, $$1<\sqrt{x}<x<y$$ and condition 1) is sufficient.

Condition 2)
If $$x = 2$$ and $$y = 3$$, then the answer is ‘yes’.
If $$x = 4$$ and $$y = 3$$, then the answer is ‘no’
Thus, condition 2) is not sufficient, since it does not yield a unique solution.

Therefore, the correct answer is A.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8456 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 25 Nov 2018, 18:36 MathRevolution wrote: [Math Revolution GMAT math practice question] (inequality) Is $$x^3-4x>0？$$ $$1) x>2$$ $$2) x>-2$$ => 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. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. $$x^3-4x>0$$ $$=> x(x^2-4)>0$$ $$=> x(x+2)(x-2)>0$$ $$=> -2<x<0$$ or $$x > 2$$ Since we have $$1$$ variable ($$x$$) and $$0$$ equations, D is most likely to be the answer. So, we should consider the conditions on their own first. Condition 1) In inequality questions, the law “Question is King” tells us that if the solution set of the question includes the solution set of the condition, then the condition is sufficient Since the solution set of the question, $$-2<x<0$$ or $$x > 2$$, includes the solution set of condition 1), $$x > 2$$, condition 1) is sufficient. Condition 2) The solution set of the question, $$-2<x<0$$ or $$x > 2$$, does not include the solution set of condition 2), $$x > -2$$, so condition 2) is not sufficient. Therefore, A is the answer. Answer: A If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8456
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

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26 Nov 2018, 00:34
[Math Revolution GMAT math practice question]

(number properties) If $$x$$ and $$y$$ are positive integers, is $$\sqrt{15xy}$$ an integer?

1) $$xy$$ is a multiple of $$15$$
2) $$x$$ and $$y$$ are prime numbers
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8456 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 27 Nov 2018, 02:39 [Math Revolution GMAT math practice question] (functions) In the x-y plane, line l passes through points $$(-1,-1)$$ and $$(3,k)$$. What is the value of $$k$$? 1) The y-intercept of line l is $$1$$ 2) The slope of line l is $$2$$ _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

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27 Nov 2018, 02:48
MathRevolution wrote:
[Math Revolution GMAT math practice question]

(functions) In the x-y plane, line l passes through points $$(-1,-1)$$ and $$(3,k)$$. What is the value of $$k$$?

1) The y-intercept of line l is $$1$$
2) The slope of line l is $$2$$

From statement 1:

y-intercept, which is C in y = mx+c. Given C = 1.
slope m = $$\frac{y_2-y_1}{x_2-x_1}$$ = $$\frac{k+1}{4}$$
y = $$\frac{k+1}{4}$$*x + 1.
using any if the points (-1,-1) or (3,k) gives k = 7.
Sufficient.

From statement 2:

Slope, m = 2.
m = $$\frac{k+1}{4}$$ = 2.
Solving gives k as 7.
Sufficient.

D is the answer.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8456
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

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28 Nov 2018, 02:06
MathRevolution wrote:
[Math Revolution GMAT math practice question]

(number properties) If $$x$$ and $$y$$ are positive integers, is $$\sqrt{15xy}$$ an integer?

1) $$xy$$ is a multiple of $$15$$
2) $$x$$ and $$y$$ are prime numbers

=>

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.

Since we have $$2$$ variables ($$x$$ and $$y$$) and $$0$$ equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
When we consider both conditions together, there are two sets of possible values of $$x$$ and $$y: x = 3, y = 5$$ and $$x = 5, y = 3$$. In both cases, $$xy = 15$$, so
$$\sqrt{15xy} = \sqrt{15*3*5} = \sqrt{225} = 15$$ is an integer.
Thus, both conditions together are sufficient.

Since this question is a statistics question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
If $$x = 3$$ and $$y = 5$$, then $$\sqrt{15xy} = \sqrt{15*3*5} = \sqrt{225} = 15$$ is an integer.
If $$x = 6$$ and $$y = 5$$, then $$\sqrt{15xy} = \sqrt{15*6*5} = \sqrt{450} = 15\sqrt{2}$$ is not an integer.
Since we don’t have a unique answer, condition 1) is not sufficient by CMT (Common Mistake Type) 2.

Condition 2)
If $$x = 3$$ and $$y = 5$$, then $$\sqrt{15xy} = \sqrt{15*3*5} = \sqrt{225} = 15$$ is an integer.
If $$x = 2$$ and $$y = 5$$, then $$\sqrt{15xy} = \sqrt{15*2*5} = \sqrt{150} = 5\sqrt{6}$$ is not an integer.
Since we don’t have a unique answer, condition 2) is not sufficient by CMT (Common Mistake Type) 2.

Therefore, C is the answer.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8456 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 28 Nov 2018, 02:07 [Math Revolution GMAT math practice question] (number properties) If $$n$$ is a positive integer, is $$\sqrt{17n}$$ an integer? 1) $$68n$$ is the square of an integer. 2) $$\frac{n}{68}$$ is the square of an integer. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8456
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

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29 Nov 2018, 02:44
MathRevolution wrote:
[Math Revolution GMAT math practice question]

(functions) In the x-y plane, line l passes through points $$(-1,-1)$$ and $$(3,k)$$. What is the value of $$k$$?

1) The y-intercept of line l is $$1$$
2) The slope of line l is $$2$$

=>

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.

Since we have $$1$$ variable ($$k$$) and $$0$$ equations in the original condition, D is most likely to be the answer. So, we should consider each condition on its own first.

We consider the equation of the line $$l, y = mx + b.$$ Since it passes through the points $$(-1,-1)$$ and $$(3,k),$$ we can plug these points into its equation to yield $$-1 = -m + b$$ and $$k = 3m + b.$$

Since we have $$3$$ variables and $$2$$ equations, D is most likely to be the answer. So, we should consider each condition on its own first.

Condition 1)
Since the y-intercept of line $$l$$ is $$1$$, we have $$b = 1$$ and $$m = b + 1 = 2.$$
Thus, $$k = 3m + b = 3*2 + 1 = 7.$$
Condition 1) is sufficient.

Condition 2)
Since the slope of line $$l$$ is $$2$$, we have $$m = 2$$ and $$b = m – 1 = 1.$$
Thus, $$k = 3m + b = 3*2 + 1 = 7.$$
Condition 2) is sufficient.

Note: When we checked the two conditions, we showed that both were equivalent in terms of b. So, each condition is sufficient by Tip 1)
of the VA method, which states that D is most likely to be the answer if conditions 1) and 2) provide the same information.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8456 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 29 Nov 2018, 02:45 [Math Revolution GMAT math practice question] (integer) If $$m$$ and $$n$$ are positive integers, what is the greatest common divisor of $$m$$ and $$n$$? $$1) m=n+1$$ $$2) m*n$$ is divisible by $$2$$ _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

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30 Nov 2018, 01:56
MathRevolution wrote:
[Math Revolution GMAT math practice question]

(number properties) If $$n$$ is a positive integer, is $$\sqrt{17n}$$ an integer?

1) $$68n$$ is the square of an integer.
2) $$\frac{n}{68}$$ is the square of an integer.

=>

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.

Modifying the question:
The question asks if $$\sqrt{17n} = a$$ for some integer a. This is equivalent to asking if $$17n = a^2$$ for some integer a.

Since we have $$1$$ variable ($$n$$) and $$0$$ equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
Since $$68n$$ is the square of an integer and $$68 = 4*17$$, we must have $$68n = 4*17*17*k^2$$ for some integer $$k$$, and $$n = 17*k^2$$ or $$17n = 17^2*k^2 = (17*k)^2.$$
Thus, $$17n$$ is the square of the integer $$17k$$, and condition 1) is sufficient.

Condition 2)
Since $$\frac{n}{68}$$ is a square of an integer and $$68 = 4*17$$, we have $$\frac{n}{68} = m^2$$ for some integer $$m$$, and $$n = 17*4*m^2$$ or $$17n = 17^2*2^2*m^2 = (34m)^2.$$
Thus, $$17n$$ is the square of the integer $$17k$$, and condition 2) is sufficient.

Therefore, D is the answer.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
_________________
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8456 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 30 Nov 2018, 01:56 [Math Revolution GMAT math practice question] (number property) If $$k$$ is a positive integer and $$n=(k-1)k(k+1)$$, is $$n$$ a multiple of $$8$$? 1) $$k$$ is an odd number 2) $$k = 1$$ _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

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30 Nov 2018, 08:45
MathRevolution wrote:
[Math Revolution GMAT math practice question]

(number property) If $$k$$ is a positive integer and $$n=(k-1)k(k+1)$$, is $$n$$ a multiple of $$8$$?

1) $$k$$ is an odd number
2) $$k = 1$$

From statement 1:

k is an odd number.
Let k be 2k+1
Then n = (2k+1-1)(2k+1)(2k+2)
n = 8k^3+12k^2+4k.
For an odd value of k. n will always be a multiple of 8.
Sufficient.

From statement 2:
k = 1.
n = 0. 0 is a multiple of 8.
Sufficient.

D is the answer.
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Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

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02 Dec 2018, 18:50
MathRevolution wrote:
[Math Revolution GMAT math practice question]

(integer) If $$m$$ and $$n$$ are positive integers, what is the greatest common divisor of $$m$$ and $$n$$?

$$1) m=n+1$$
$$2) m*n$$ is divisible by $$2$$

=>

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.

Since two consecutive integers are always relatively prime, the greatest common divisor of m and n is 1. Thus, condition 1) is sufficient.

Condition 2)
If $$m = 2$$ and $$n = 3$$, then the greatest common divisor of $$m$$ and $$n$$ is $$1$$.
If $$m = 2$$ and $$n = 4,$$ then the greatest common divisor of $$m$$ and $$n$$ is $$2$$.
Thus, condition 2) is not sufficient since it does not yield a unique solution.

Therefore, the correct answer is A.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8456 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 02 Dec 2018, 19:01 MathRevolution wrote: [Math Revolution GMAT math practice question] (number property) If $$k$$ is a positive integer and $$n=(k-1)k(k+1)$$, is $$n$$ a multiple of $$8$$? 1) $$k$$ is an odd number 2) $$k = 1$$ => 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. Since we have $$2$$ variables ($$n$$ and $$k$$) and $$1$$ equation, D is most likely to be the answer. So, we should consider each condition on its own first. Condition 1) Since $$k$$ is an odd number, $$k – 1$$ and $$k + 1$$ are consecutive even integers. Any product of consecutive even integers is a multiple of $$8$$. Thus, condition 1) is sufficient. Condition 2) Since $$k = 1$$, we have $$n = (k-1)k(k+1) = 0*1*2 = 0. 0$$ is a multiple of any number, so $$n = 0$$ is a multiple of $$8$$. Thus, condition 2) is sufficient. Therefore, D is the answer. Answer: D Since this question is a CMT4(B) question. Condition 2) is easy to understand and condition 1) is hard. When one condition is easy to understand, and the other is hard, D is most likely to be the answer. If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
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Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS   [#permalink] 02 Dec 2018, 19:01

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