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27 Oct 2021, 05:30
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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:
55%
(hard)
Question Stats:
56% (01:53) correct
44%
(01:54)
wrong
based on 190
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If n is a prime number, does n = 17?
(1) n − 1 = m^4, where m is an integer.
(2) n^2 < 300
(1) n − 1 = m^4, where m is an integer.
(2) n^2 < 300
27 Oct 2021, 05:45
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If n is a prime number, does n = 17?
(1) n − 1 = m^4, where m is an integer.
For m = 1, n =2 and for m=2, n=17 - Insufficient
(2) n^2 < 300
n can be any prime number, 2, 5, 7 etc - Insufficient
Combined we get that if n = 2, then n^2 = 4 and it is < 300 and even if n = 17 we get n^2 = 289
Even with (1) and (2) it is insufficient
(1) n − 1 = m^4, where m is an integer.
For m = 1, n =2 and for m=2, n=17 - Insufficient
(2) n^2 < 300
n can be any prime number, 2, 5, 7 etc - Insufficient
Combined we get that if n = 2, then n^2 = 4 and it is < 300 and even if n = 17 we get n^2 = 289
Even with (1) and (2) it is insufficient
27 Oct 2021, 11:30
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Bunuel
If n is a prime number, does n = 17?
(1) n − 1 = m⁴, where m is an integer.
(2) n² < 300
(1) n − 1 = m⁴, where m is an integer.
(2) n² < 300
Given: n is a prime number
Target question: Does n = 17?
Statement 1: n − 1 = m⁴, where m is an integer.
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of n and m that satisfy statement 1 (and the given information, which says n is prime). Here are two:
Case a: n = 2 and m = 1. In this case, the answer to the target question is NO, n does not equal 17
Case b: n = 17 and m = 2. In this case, the answer to the target question is YES, n equals 17
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: n² < 300
Pro tip: Rather than try to find values of n that satisfy statement 2, we can save some time by checking to see whether we can REUSE any of the values we used for statement 1.
In this case, it turns out that we can reuse both pairs values, since the n-values in both pairs also satisfy statement 2 (i.e., 2² < 300 and 17² < 300)
So, we have:
Case a: n = 2. In this case, the answer to the target question is NO, n does not equal 17
Case b: n = 17. In this case, the answer to the target question is YES, n equals 17
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.
In other words,
Case a: n = 2 and m = 1. In this case, the answer to the target question is NO, n does not equal 17
Case b: n = 17 and m = 2. In this case, the answer to the target question is YES, n equals 17
Since we can’t answer the target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent
