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20 Nov 2015, 15:21
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
69% (02:12) correct
31%
(02:11)
wrong
based on 619
sessions
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Not Attempted Yet
QUANT 4-PACK SERIES Data Sufficiency Pack 4 Question 2 Z is a positive integer...
Z is a positive integer greater than 3. How many distinct prime factors does (Z + 1)(Z – 1) have?
1) Z is not even
2) Z is not a multiple of 5
48 Hour Window Answer & Explanation Window
Earn KUDOS! Post your answer and explanation.
OA, and explanation will be posted after the 48 hour window closes.
This question is part of the Quant 4-Pack series
Scroll Down For Official Explanation
Z is a positive integer greater than 3. How many distinct prime factors does (Z + 1)(Z – 1) have?
1) Z is not even
2) Z is not a multiple of 5
48 Hour Window Answer & Explanation Window
Earn KUDOS! Post your answer and explanation.
OA, and explanation will be posted after the 48 hour window closes.
This question is part of the Quant 4-Pack series
Scroll Down For Official Explanation
20 Nov 2015, 15:43
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EMPOWERgmatRichC
Target question: How many distinct prime factors does (Z + 1)(Z – 1) have?
Given: Z is a positive integer greater than 3
Statement 1: Z is not even
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of Z that satisfy statement 1. Here are two:
Case a: Z = 9, in which case (Z + 1)(Z - 1) = (10)(8) = 80 = (2)(2)(2)(2)(5). In this case, we have TWO distinct prime factors
Case b: Z = 11, in which case (Z + 1)(Z - 1) = (12)(10) = 120 = (2)(2)(2)(3)(5). In this case, we have THREE distinct prime factors
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values
Statement 2: Z is not a multiple of 5
This statement doesn't FEEL sufficient either, so I'll TEST some values.
There are several values of Z that satisfy statement 2. Here are two:
Case a: Z = 9, in which case (Z + 1)(Z - 1) = (10)(8) = 80 = (2)(2)(2)(2)(5). In this case, we have TWO distinct prime factors
Case b: Z = 11, in which case (Z + 1)(Z - 1) = (12)(10) = 120 = (2)(2)(2)(3)(5). In this case, we have THREE distinct prime factors
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Notice that I used the same values of Z for the first 2 statements. This means that the same Z-values satisfy BOTH statements.
That is:
Case a: Z = 9, in which case (Z + 1)(Z - 1) = (10)(8) = 80 = (2)(2)(2)(2)(5). In this case, we have TWO distinct prime factors
Case b: Z = 11, in which case (Z + 1)(Z - 1) = (12)(10) = 120 = (2)(2)(2)(3)(5). In this case, we have THREE distinct prime factors
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT
Answer = E
Cheers,
Brent
General Discussion
22 Nov 2015, 01:42
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
Z is a positive integer greater than 3. How many distinct prime factors does (Z + 1)(Z – 1) have?
1) Z is not even
2) Z is not a multiple of 5
There is one variable (z) and 2 equations are given by the 2 conditions, increasing the chance (D) will be our answer.
For condition 1, z=3, (3+1)(3-1)=8=2^3, the no. of distinct prime factors:1
z=7, (7+1)(7-1)=(2^4)3, the no. of distinct prime factors: 2
For condition 2, z=3, (3+1)(3-1)=8=2^3, the no. of distinct prime factors:1
z=7, (7+1)(7-1)=(2^4)3, the no. of distinct prime factors: 2
Looking at the conditions together,
z=3, (3+1)(3-1)=8=2^3, the no. of distinct prime factors:1
z=7, (7+1)(7-1)=(2^4)3, the no. of distinct prime factors: 2.
Therefore, the answer becomes (E).
For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
Z is a positive integer greater than 3. How many distinct prime factors does (Z + 1)(Z – 1) have?
1) Z is not even
2) Z is not a multiple of 5
There is one variable (z) and 2 equations are given by the 2 conditions, increasing the chance (D) will be our answer.
For condition 1, z=3, (3+1)(3-1)=8=2^3, the no. of distinct prime factors:1
z=7, (7+1)(7-1)=(2^4)3, the no. of distinct prime factors: 2
For condition 2, z=3, (3+1)(3-1)=8=2^3, the no. of distinct prime factors:1
z=7, (7+1)(7-1)=(2^4)3, the no. of distinct prime factors: 2
Looking at the conditions together,
z=3, (3+1)(3-1)=8=2^3, the no. of distinct prime factors:1
z=7, (7+1)(7-1)=(2^4)3, the no. of distinct prime factors: 2.
Therefore, the answer becomes (E).
For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
