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# The Ultimate Q51 Guide [Expert Level]

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Math Revolution GMAT Instructor
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]

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21 Feb 2017, 18:50
What is the difference between the circumferences of 2 circles such that the diameters of the circles are 10 and 11?

A. $$\frac{π}{2}$$
B. $$π$$
C. $$\frac{3π}{2}$$
D. $$2π$$
E. $$\frac{5π}{2}$$

==> The circumference of a circle is πd, thus $$π(11-10)= π$$. Therefore, the answer is B.
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]

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23 Feb 2017, 20:30
John traveled 150 miles. What is the average speed of John on the trip?

1) John traveled the first 100 miles at the rate of 50 miles per hour
2) John traveled the last 100 miles at the rate of 50 miles per hour

==> In the original condition, he travels the total 150 miles by dividing it to two trips of 50 miles each. Hence, since there are 6 variables, E is most likely to be the answer. In order for C to be the answer, there must be a word “constant rate” mentioned.

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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]

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26 Feb 2017, 21:36
When a positive integer n is divided by 2, what is the remainder?
1) The remainder is 1 when n is divided by 5
2) The remainder is 1 when n is divided by 10

==> 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 can solve it by using direct substitution.
For con 1), from n=5p+1(p=any positive integer), you get n=1,6,… However, from n=1=2(0)+1, you get r=1, but n=6=2(3)+0, you get r=0, hence it is not unique and not sufficient.
For con 2), from n=10q+1(q=any positive integer), you get n=1,11,21,… However, for all cases, the remainder=1, hence it is unique and sufficient.

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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]

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01 Mar 2017, 18:56
What is the difference between the hypotenuse’s length of the right triangle with 2 shorter sides of 10 and 24 and the hypotenuse’s length of the right triangle with 2 shorter sides of 7 and 24?

A. 1
B. 2
C. 3
D. 4
E. 5

==>For Pythagorean Theorem, 5:12:13=10:24:26 and 7:24:25 appear most frequently. Thus, the length of hypotenuse each becomes 26 and 25, and the difference becomes 26-25=1.

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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.

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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]

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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.

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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.
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]

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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.
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]

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09 Mar 2017, 22:37
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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.

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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]

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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.
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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.

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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 $$\frac{0-(-6)}{-3-0=-2}$$

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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).

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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Re: The Ultimate Q51 Guide [Expert Level]   [#permalink] 30 Mar 2017, 18:33

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# The Ultimate Q51 Guide [Expert Level]

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