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Math Revolution GMAT Instructor
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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02 Mar 2017, 18:31
\((xy)^2=?\) 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 \((xy)^2=4\), hence it is unique and sufficient. Therefore, the answer is C. Answer: C
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Math Revolution GMAT Instructor
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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. Therefore, the answer is E. Answer: E
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Math Revolution GMAT Instructor
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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06 Mar 2017, 18:18
\((x+y)^2(xy)^2=?\) 1) xy=5 2) x+y=6 ==> If you modify the original condition and the question, \((x+y)^2(xy)^2=?\) becomes (x+yx+y)(x+y+xy)=?, 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. Answer: A
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Math Revolution GMAT Instructor
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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. Answer: E
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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09 Mar 2017, 22:37
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. Answer: C
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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. Answer: A
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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. Answer: C
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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15 Mar 2017, 18:39
In the xy plane, what is the slope between yintercept and a negative xintercept of \(y=x^2+x6\)? A. 2 B. 3 C. 2 D. 4 E. 6 ==> From y=x2+x6=(x+3)(x2)=0, the xintercept becomes (3,0) or (2,0), and (0,6). From these, the negative xintercept is (3,0) and the negative yintercept is (0,6). The slope of the straight line that passes through the two points becomes \(\frac{0(6)}{30=2}\) The answer is A. Answer: A
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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. mn+1 C. (m1)(n1) D. (m+1)(n+1) E. mn ==> The number of factors of \(3^m7^n\) becomes (m+1)(n+1). The answer is D. Answer:D
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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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. Therefore, the answer is B. Answer: B
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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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. Therefore, the answer is C. Answer: C
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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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. Therefore, the answer is B. Answer: B
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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26 Mar 2017, 18:34
In the xy plane there is a line K, (x/a)+(y/b)=1. What is the xintercept of line K? 1) a=b 2) a=1 ==> If you modify the original condition and the question, the xintercept 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. Answer: B
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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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. Therefore, the answer is D. Answer: D
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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. Answer: B
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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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. Therefore, the answer is C. Answer: C
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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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=2x5 B. y=6x5 C. y=(x/2)5 D. y=(x/3)5 E. y=(2x5)/3 ==> According to the Ivy Approach, you get is:”=” and greater than:”+”, so you get 2x=5+3y. From 3y=2x5, y=(2x5)/3, the answer is E. Answer: E
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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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
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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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. Answer: A
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Re: The Ultimate Q51 Guide [Expert Level] [#permalink]
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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
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