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# The Ultimate Q51 Guide [Expert Level]

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5267
GMAT 1: 800 Q59 V59
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level] [#permalink]

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02 Mar 2017, 18:31
$$(x-y)^2=?$$

1) x and y are integers
2) xy=3

==> In the original condition, there are 2 variables (x, y) and in order to match the number of variables to the number of equations, there must be 2 equations. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. By solving con 1) and con 2), you get (x,y)=(1,3),(3,1),(-1,-3),(-3,-1), and all become $$(x-y)^2=4$$, hence it is unique and sufficient.

Therefore, the answer is C.
_________________

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 3 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: 5267 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: The Ultimate Q51 Guide [Expert Level] [#permalink] ### Show Tags 05 Mar 2017, 18:24 What is the scope including 1/11+1/12+1/13+......+1/20? A 1/6~1/5 B. 1/5~1/4 C. 1/4~1/3 D. 1/3~1/2 E. 1/2~1 The sum of consecutive reciprocal number sequence is decided by the first number and the last number. Thus, from 10/20=1/11+1/12+.....+1/20<1/11+1/12+.....+1/20<1/11+1/12+.....+1/20=10/11, you get 1/2=10/20<1/11+1/12+.....+1/20<10/11<1, which becomes 1/2~1. Therefore, the answer is E. Answer: 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 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5267
GMAT 1: 800 Q59 V59
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level] [#permalink]

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06 Mar 2017, 18:18
$$(x+y)^2-(x-y)^2=?$$

1) xy=5
2) x+y=6

==> If you modify the original condition and the question, $$(x+y)^2-(x-y)^2=?$$ becomes (x+y-x+y)(x+y+x-y)=?, and if you simplify this, you get (2y)(2x)=?, 4xy=?. Thus, for con 1), you get xy=5, hence it is unique and sufficient. The 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 3 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: 5267 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: The Ultimate Q51 Guide [Expert Level] [#permalink] ### Show Tags 08 Mar 2017, 18:26 Is a=b? 1) a^2=b^2 2) a=2 ==> In the original condition, there are 2 variables (a,b) and in order to match the number of variables to the number of equations, there must be 2 equations. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. By solving con 1) and con 2), from a=2, you get b2=22=4, then b=±2. Thus, (a,b)=(2,2) yes but (a,b)=(2,-2) no, hence it is not sufficient. The answer is E. Answer: 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 3 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: 5267
GMAT 1: 800 Q59 V59
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level] [#permalink]

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09 Mar 2017, 22:37
Expert's post
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BOOKMARKED
What is the perimeter of a certain right triangle?

1) The hypotenuse’s length is 10
2) The triangle’s area is 24

==> In the original condition, for a right triangle, there are 2 variables (2 legs) and in order to match the number of variables to the number of equations, there must be 2 equations. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. By solving con 1) and con 2), you get 6:8:10 and the perimeter of the right triangle becomes 6+8+10=24, hence unique and sufficient.

Therefore, the answer is C.
_________________

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 3 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: 5267 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: The Ultimate Q51 Guide [Expert Level] [#permalink] ### Show Tags 12 Mar 2017, 18:51 $$Let A=6^2^0, B=2^6^0, and C=4^5^0.$$ Which of the following is true? A. A<B<C B. A<C<B C. B<A<C D. B<C<A E. C<B<A ==> You can compare the big and small numbers by making the base or the exponent the same. From$$A=6^2^0, B=2^6^0=(2^3)^2^0=8^2^0$$, you get 6<8, which becomes A<B, and from $$B=2^6^0=(2^2)^3^0=4^3^0, C=4^5^0,$$ you get 30<50, which becomes B<C. Thus, you get A<B<C. The answer is A. Answer: 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 3 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: 5267
GMAT 1: 800 Q59 V59
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level] [#permalink]

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13 Mar 2017, 18:28
$$\frac{5.09}{0.149}$$ is closest to which of the following?

A. 0.34
B. 3.4
C. 34
D. 340
E. 3,400

From $$\frac{5.09}{0.149} = \frac{5.10}{0.15} = \frac{510}{15} =34$$, the answer is C.

_________________

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 3 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: 5267 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: The Ultimate Q51 Guide [Expert Level] [#permalink] ### Show Tags 15 Mar 2017, 18:39 In the x-y plane, what is the slope between y-intercept and a negative x-intercept of $$y=x^2+x-6$$? A. -2 B. -3 C. 2 D. 4 E. 6 ==> From y=x2+x-6=(x+3)(x-2)=0, the x-intercept becomes (-3,0) or (2,0), and (0,-6). From these, the negative x-intercept is (-3,0) and the negative y-intercept is (0,-6). The slope of the straight line that passes through the two points becomes $$\frac{0-(-6)}{-3-0=-2}$$ The answer is A. Answer: 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 3 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: 5267
GMAT 1: 800 Q59 V59
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level] [#permalink]

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16 Mar 2017, 18:21
If m and n are positive integers, what is the number of factors of $$3^m7^n$$?

A. mn+m+n
B. m-n+1
C. (m-1)(n-1)
D. (m+1)(n+1)
E. mn

==> The number of factors of $$3^m7^n$$ becomes (m+1)(n+1).

The answer is D.
_________________

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 3 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: 5267 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: The Ultimate Q51 Guide [Expert Level] [#permalink] ### Show Tags 20 Mar 2017, 03:44 Is a positive integer n a multiple of 12 1) n is a multiple of 6 2) n is a multiple of 24 ==> In the original condition, there is 1 variable (n) and in order to match the number of variables to the number of equations, there must be 1 equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer. For remainder questions, you always use direct substitution. For con 1), n=6 no, n=12 yes, hence not sufficient. For con 2), n=24,48,…, hence it is always yes and sufficient. Therefore, the answer is B. Answer: B _________________ 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 3 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: 5267
GMAT 1: 800 Q59 V59
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level] [#permalink]

### Show Tags

20 Mar 2017, 18:48
Is x>y>z?
1) x>y
2) y>z

==> In the original condition, there are 3 variables (x,y,z) and in order to match the number of variables to the number of equations, there must be 3 equations. Since there is 1 for con 1) and 1 for con 2), E is most likely to be the answer. By solving con 1) and con 2), from x>y>z, it is always yes and sufficient.

Therefore, the answer is C.
_________________

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 3 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: 5267 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: The Ultimate Q51 Guide [Expert Level] [#permalink] ### Show Tags 22 Mar 2017, 18:33 Is a positive integer x a factor of 24? 1) 3x is a factor of 48 2) 2x is a factor of 24 ==> In the original condition, there is 1 variable (x) and in order to match the number of variables to the number of equations, there must be 1 equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer. For con 1), x is a factor of 16, so x=8 yes, x=16 no, hence not sufficient. For con 2), x is a factor of 12, so it is always yes, hence sufficient. Therefore, the answer is B. Answer: B _________________ 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 3 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: 5267
GMAT 1: 800 Q59 V59
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level] [#permalink]

### Show Tags

26 Mar 2017, 18:34
In the x-y plane there is a line K, (x/a)+(y/b)=1. What is the x-intercept of line K?

1) a=b
2) a=1

==> If you modify the original condition and the question, the x-intercept is the value of x when y=0, hence from (x/a)=1, you get x=a, so you only need to find a.

Therefore, the answer is B.
_________________

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 3 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: 5267 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: The Ultimate Q51 Guide [Expert Level] [#permalink] ### Show Tags 27 Mar 2017, 18:05 If the average (arithmetic mean) of 5 consecutive multiples of 5 is 30, what is the smallest number of them? A. 5 B. 10 C. 15 D. 20 E. 25 ==> If the average of 5 consecutive multiples of 5 is 30, from 20,25,30,35,40, the smallest multiple of 5 becomes 20. Therefore, the answer is D. Answer: D _________________ 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 3 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: 5267
GMAT 1: 800 Q59 V59
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level] [#permalink]

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29 Mar 2017, 18:52
If Tom goes y miles in x hours, how many miles does he go per minute, in terms of x and y?

A. 60x/y
B. y/60x
C. 60y/x
D. x/60y
E. 60xy

==>You get miles:hours=y(miles):x(hours)=y(miles):60x(minutes), and from y:60x=some:1, you get some=y/60x.

The answer is B.
_________________

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 3 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: 5267 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: The Ultimate Q51 Guide [Expert Level] [#permalink] ### Show Tags 30 Mar 2017, 18:33 m=? 1) 5 is a factor of m 2) m is a prime number ==> In the original condition, there is 1 variable (m) and in order to match the number of variables to the number of equations, there must be 1 equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer. For con 1), from m=5,10…, it is not unique and not sufficient. For con 2), from m=5,7…, it is not unique and not sufficient. By solving con 1) and con 2), you get m=5, hence it is unique and sufficient. Therefore, the answer is C. Answer: C _________________ 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 3 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: 5267
GMAT 1: 800 Q59 V59
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level] [#permalink]

### Show Tags

02 Apr 2017, 18:25
If two times x is 5 greater than three times y, what is the value of y, in terms of x?

A. y=2x-5
B. y=6x-5
C. y=(x/2)-5
D. y=(x/3)-5
E. y=(2x-5)/3

==> According to the Ivy Approach, you get is:”=” and greater than:”+”, so you get 2x=5+3y. From 3y=2x-5, y=(2x-5)/3, the answer is 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 3 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: 5267 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: The Ultimate Q51 Guide [Expert Level] [#permalink] ### Show Tags 04 Apr 2017, 06:49 Is x<1<y? 1) x<√x<y 2) x<√y<y ==> In the original condition, there are 2 variables (x,y) and in order to match the number of variables to the number of equations, there must be 2 equations. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. By solving con 1) and con 2), from x<√x, you get 0<x<1, and from √y<y, you get y>1. Then, you get x<1<y, hence always yes. The answer is C. Answer: C _________________ 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 3 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: 5267
GMAT 1: 800 Q59 V59
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level] [#permalink]

### Show Tags

06 Apr 2017, 18:30
[m] is defined as the greatest integer less than or equal to m, what is the value of [m]?

1) 1<m<2
2) |m|<1

==> In the original condition, there is 1 variable (m) and in order to match the number of variables to the number of equations, there must be 1 equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer.
For con 1), from [m]=1, it is unique and sufficient.
For con 2), from -1<m<1, you get [0]=0, but from [0.1]=-1, it is not unique and not sufficient.

Therefore, the 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 3 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: 5267 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: The Ultimate Q51 Guide [Expert Level] [#permalink] ### Show Tags 09 Apr 2017, 18:39 If 1 male, 2 females, and 1 child are to be selected at random from 8 males, 10 females, and 8 children, respectively, how many such cases are possible? A. 980 B. 1,440 C. 1,880 D. 2,480 E. 2,880 ==> From (8C1)(10C2)(8C1)=(8)(10*9/2!)(8)=2,880, the answer is E. Answer: 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 3 month Online Course"
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"Unlimited Access to over 120 free video lessons - try it yourself"

Re: The Ultimate Q51 Guide [Expert Level]   [#permalink] 09 Apr 2017, 18:39

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# The Ultimate Q51 Guide [Expert Level]

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