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Intern
Joined: 03 Jan 2023
Posts: 4
Given Kudos: 18
GMAT 1: 610 Q36 V38
If n is a positive integer, what is the value of n?
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07 Jul 2023, 10:44
07 Jul 2023, 10:44
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If n is a positive integer, what is the value of n?
(1) For any positive integer y, the product of all integers from y to y+n is divisible by 35.
(2) n^2 - 8n + 7 < 0
(1) For any positive integer y, the product of all integers from y to y+n is divisible by 35.
(2) n^2 - 8n + 7 < 0
Re: If n is a positive integer, what is the value of n?
[#permalink]
07 Jul 2023, 18:30
07 Jul 2023, 18:30
1
Kudos
gmatophobia wrote:
(1) For any positive integer y, the product of all integers from y to y+n is divisible by 35.
35 = 7 * 5
Hence, if we take any set of 7 consecutive integers, the product will be divisible by 35.
Therefore, the minimum value of 'n' is 6. Any value of n greater than or equal to 6 satisfies statement 1.
Hence, the statement alone is not sufficient to find a unique value of n. We can eliminate A and D.
35 = 7 * 5
Hence, if we take any set of 7 consecutive integers, the product will be divisible by 35.
Therefore, the minimum value of 'n' is 6. Any value of n greater than or equal to 6 satisfies statement 1.
Hence, the statement alone is not sufficient to find a unique value of n. We can eliminate A and D.
If y=2, n=5, y+n=7
2*3*4*5*6*7 is divisible by 35.
What am I doing wrong here?
Quant Chat Moderator
Joined: 22 Dec 2016
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Re: If n is a positive integer, what is the value of n?
[#permalink]
07 Jul 2023, 13:44
07 Jul 2023, 13:44
OmkarSheth008 wrote:
If n is a positive integer, what is the value of n?
(1) For any positive integer y, the product of all integers from y to y+n is divisible by 35.
(2) n^2 - 8n + 7 < 0
(1) For any positive integer y, the product of all integers from y to y+n is divisible by 35.
(2) n^2 - 8n + 7 < 0
Statement 1
(1) For any positive integer y, the product of all integers from y to y+n is divisible by 35.
35 = 7 * 5
Hence, if we take any set of 7 consecutive integers, the product will be divisible by 35.
Therefore, the minimum value of 'n' is 6. Any value of n greater than or equal to 6 satisfies statement 1.
Hence, the statement alone is not sufficient to find a unique value of n. We can eliminate A and D.
Statement 2
(2) \(n^2 - 8n + 7 < 0\).
\(n^2 - 8n + 7 < 0\)
\((n-1)(n-7) < 0\)
------------ 1 ------------------------ 7 -------------
Any integer value between 1 and 7 satisfies the inequality. The statement alone is not sufficient to find a unique value of n. We can eliminate B.
Combined
From statement 1: \(n\geq6\)
From statement 2: \(1 < n < 7\)
The only common value = 6.
The statements combined help us identify a unique value of n.
Option C
