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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8003
GMAT 1: 760 Q51 V42 GPA: 3.82
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n=?
1) n^2=1
2) n^3=1

ANS: In the original condition, there is 1 variable (n) and there is a high chance that D is the correct answer.
In condition 1), we get n=-1 and 1. The answer is not unique and the condition is not sufficient.
In condition 2), we only have n=1. The answer is not unique and the condition is sufficient. Hence, the correct answer is B.
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Math Revolution GMAT Instructor V
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Posts: 8003
GMAT 1: 760 Q51 V42 GPA: 3.82
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Is a positive integer x a prime number?
1) All the prime factors of x are greater than √x
2) All the prime factors of x are 1 and itself

ANS: The original condition has 1 variable (x) and there is a high chance that D is the correct answer. Con 1) and con 2) both are the definition of prime number. Hence, the correct answer is D.
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Math Revolution GMAT Instructor V
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GMAT 1: 760 Q51 V42 GPA: 3.82
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Is |a|=|b|?
1) a+b=0
2) a-b=2

*Answer: If we modify the original condition and the question, we get a=±b?. Since the condition 1) is a=-b, the answer is yes and the correct answer is A.
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Math Revolution GMAT Instructor V
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Posts: 8003
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u=?
1) |u|+|v|=0
2) u^2+v^2=0

*ANS: Since there are 2 variables in the original condition, there is a high chance that C is the correct answer. Using 1) & 2), we get 1)=2). Then, u=v=0. Hence, the correct answer is D.
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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8003
GMAT 1: 760 Q51 V42 GPA: 3.82
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Is 16 contained in the set S?
1) All the elements in the set S are the multiples of 4
2) All the elements in the set S are the square of integers

*ANS: In the original condition, we have to find out all elements of the set S. Since there are many variables, there is a high chance that E is the correct answer. Using 1) & 2), we get S={16}. The answer is yes. When S={4}, the answer is no and the condition is not sufficient. Hence, the correct answer is E.
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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8003
GMAT 1: 760 Q51 V42 GPA: 3.82
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Is |x|=y+1?
1) y+x=-1
2) x<0

*ANS: Since there are 2 variables (x and y) in the original condition, there is a high chance that C is the correct answer. Using 1) & 2), we get |x|=-x (when x<0). So from -x=y+1?, x+y=-1?, the answer is yes and the condition is sufficient. Hence, the correct answer is C.
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Math Revolution GMAT Instructor V
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Posts: 8003
GMAT 1: 760 Q51 V42 GPA: 3.82
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Is x<1/y?
1) y>0
2) xy<1

ANS: If we modify the original condition and the question, in case of inequality, square is very important. If we multiply y^2 to both sides, we get xy^2<y?, xy^2-y<0?, y(xy-1)<0?. There are 2 variables (x and y) and there is a high chance that C is the correct answer. Using 1) & 2), the answer is always yes and the condition is sufficient. Thus, the correct answer is C.
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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8003
GMAT 1: 760 Q51 V42 GPA: 3.82
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What is the number of multiples of 4 in 5 consecutive integers?
1) The median of them is 4
2) The average (arithmetic mean) of them is a multiple of 4

ANS: There is one variable in the original (n, n+1, n+2, n+3, n+4). Hence, the correct answer is D.
Since , 1)=2), the answer is unique and the condition is sufficient. Hence, the correct answer is D. If we apply the common mistake type 4(B), the answer is D.
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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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Is ∣x∣<1?
1) x=1/(3+y^2)
2) y=-2
*ANS: There are 2 variables in the original condition. Hence there is a high chance that C is the correct answer. If we apply the common mistake type 4(A) just like tip 4. In case of con 1), we always get y^2≥0. So, from 0<x=1/(3+y^2)≤1/3<1, the answer is yes and the condition is sufficient. The correct answer, thus, is A.
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If a and b are positive integers, is ab an even?
1) (a+1)b=even
2) (a+1)^b=odd

*ANS: Since there are 2 variables in the original condition, the answer is C. However, we have to apply common mistake type 4(A) because it is one of key questions. In case of con 2), from a+1=odd, a=even, the answer is always yes and the condition is sufficient. Hence, the correct answer is B.
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Math Revolution GMAT Instructor V
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x percent of what number is equal to y?
1) x=10y
2) xy=40

ANS: If we modify the original condition and the question, we get x(1/100)(some)=y. So we have to find x/y. In case of condition 1), we get x/y=10. The condition is sufficient and the correct answer is A.
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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42 GPA: 3.82
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When a person went to travelling, she estimated the traveled distance and the speed. Then, she calculated the actual time. Is the difference between estimated and actual time smaller than 10minutes?
1) The difference between the estimated and actual distance is within 50miles
2) The difference between the estimated and actual velocity is within 50miles/1minutes

ANS: There are 6 variables (estimated: v1, t1, d1, actual; v2, t2, d2) in the original condition, and 2 equations (estimated: v1t1=d1, actual; v2t2=d2). Hence, the correct answer is E.
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GMAT 1: 760 Q51 V42 GPA: 3.82
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Both a set S and a set P have the same number of elements. Is a standard deviation of the set P smaller than the standard deviation of the set S?
1) All elements of the set P is multiples of 3.
2) All elements of the set S is multiples of 9.

ANS: From the original condition, we have to know all elements of the set S. Hence, there is a high chance that E is the correct answer. Using 1) & 2), P={3,6,9}, S={9,18,27} yes, P={3, 30,300}, S={9,18,27} no. Hence, the conditions are not sufficient, and the correct answer is E.
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Math Revolution GMAT Instructor V
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Posts: 8003
GMAT 1: 760 Q51 V42 GPA: 3.82
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Which of the x, 1/x, x^2 is the greatest?
1) x^2-x<0
2) |x|<1

ANS: In the original condition, there is one variable, x. Hence, there is a high chance that D is the correct answer. In case of condition 1), from x(x-1)<0, we get 0<x<1. Hence, 1/x is always greater. The answer is unique and the condition is sufficient. In case of condition 2), from -1<x<1, if x=0.1, 1/x is the greatest. However, if x=-0.1, x^2 is always greatest. The answer is not unique and the condition is not sufficient. The correct answer is A.
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MathRevolution wrote:
How many 5 existed in the 11 numbers?
1) The average (arithmetic mean) of the 11 numbers is 5
2) The median of the 11 numbers is 5

*ANS: If we modify the original condition and the question, since we have 11 numbers, the median exists in these numbers. Hence, if we look at the condition 2), since the median is 5, 5 is always a part of 11 numbers. The answer is yes and the answer is B.

I understood the question stem as "How many 5s are there in the set of 11 numbers?"
However, the answer is explained for "Whether 5 existed in the set of 11 numbers?"

Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8003
GMAT 1: 760 Q51 V42 GPA: 3.82
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Is x^2 > y^2?

(1) x + y = 2
(2) x > y

==> In the original condition, C is highly likely to be an answer since the variable becomes two (x,y). 1) & 2), x^2-y^2>0?, in (x-y)(x+y)>0? you get x-y>0, and thus x+y=2>0. The answer is always yes, therefore suffi. Hence, the answer is C.

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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8003
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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Is x^2>y^2?
1) x+y=2
2) x>y

==> In the original condition, C is highly likely to be an answer since the variable becomes two (x,y). 1) & 2), x^2-y^2>0?, in (x-y)(x+y)>0? you get x-y>0, and thus x+y=2>0. The answer is always yes, therefore suffi. Hence, the answer is C.

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1
Is m/n>0?
1) m+n>0
2) mn>0
==> If you change the original condition and problems, in the case of sign of inequality, squaring is the most important thing because squaring never changes the direction of the sign of inequality even if it’s divided or multiplied since any number squared is a positive number. Hence, if you multiply n^2 by both sides, you get n2(m/n)>n2*0? --> mn>0?. Therefore, the answer is B.
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MathRevolution wrote:
u=?
1) |u|+|v|=0
2) u^2+v^2=0

*ANS: Since there are 2 variables in the original condition, there is a high chance that C is the correct answer. Using 1) & 2), we get 1)=2). Then, u=v=0. Hence, the correct answer is D.

Hi
I see 2 variables in con1& con 2
But orig condition has only one variable :u
No eq , need 1 eq , so isn't it D?

2nd how did you compute 1)= 2)?

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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8003
GMAT 1: 760 Q51 V42 GPA: 3.82
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If 2ab is a 3 digit integer, is 2ab divisible by 3?
1) b=3 .
2) 2+a+b is divisible by 9.

==> In the original condition, the answer is C with two variables (a, b). However, since it is a integer problem that is a key question, if you apply CMT 4(A), in the case of 2) if 2+a+b is divided by 9, 3 digit integer 2ab is divided by 9, and it means it can also be divided by 3, hence yes, and suffi. Therefore, the answer is B.

_________________ Re: Math Revolution Approach (DS)   [#permalink] 29 Sep 2016, 06:42

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