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For an integer n greater than 1, n* denotes the product of

by AAPL » Tue May 08, 2018 4:34 am

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For an integer n greater than 1, n* denotes the product of all the integers from 1 to n inclusive. How many prime numbers are there between 7*+2 and 7*+7, inclusive?

A. 0
B. 1
C. 2
D. 3
E. 4

The OA is A.

This is an approach,

None. As 7! is multiple of all numbers in the set 1, 2, 3, 4, 5, 6, 7, so when you add any of these numbers to the 7! you will always a multiple of one the numbers in the set.

Has anyone another approach to solve this PS question? Regards!
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by Brent@GMATPrepNow » Tue May 08, 2018 5:12 am
AAPL wrote:For an integer n greater than 1, n* denotes the product of all the integers from 1 to n inclusive. How many prime numbers are there between 7*+2 and 7*+7, inclusive?

A. 0
B. 1
C. 2
D. 3
E. 4
7* = 7! = (7)(6)(5)(4)(3)(2)(1)

So, 7* + 2 = (7)(6)(5)(4)(3)(2)(1) + 2
= 2[(7)(6)(5)(4)(3)(1) + 1]
= some multiple of 2
So, 7* + 2 is NOT a prime number

7* + 3 = (7)(6)(5)(4)(3)(2)(1) + 3
= 3[(7)(6)(5)(4)(2)(1) + 1]
= some multiple of 3
So, 7* + 3 is NOT a prime number

7* + 4 = (7)(6)(5)(4)(3)(2)(1) + 4
= 4[(7)(6)(5)(3)(2)(1) + 1]
= some multiple of 4
So, 7* + 4 is NOT a prime number
.
.
.
.
7* + 7 = (7)(6)(5)(4)(3)(2)(1) + 7
= 7[(6)(5)(4)(3)(2)(1) + 1]
= some multiple of 7
So, 7* + 7 is NOT a prime number

ASIDE: You can assume that I was able to perform the same steps with 7* + 5 and 7* + 6

Answer: A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Scott@TargetTestPrep » Wed May 09, 2018 3:54 pm
AAPL wrote:For an integer n greater than 1, n* denotes the product of all the integers from 1 to n inclusive. How many prime numbers are there between 7*+2 and 7*+7, inclusive?

A. 0
B. 1
C. 2
D. 3
E. 4
We can see that n* actually means n!. So, 7*+ 2 = 7! + 2 and 7* + 7 = 7! + 7. Therefore, we need to determine the number of prime numbers between 7! + 2 and 7! + 7, inclusive.

The numbers between 7! + 2 and 7! + 7, inclusive, are:

7! + 2, 7! + 3, 7! + 4, 7! + 5, 7! + 6 and 7! + 7

Let's see which one(s) of these numbers are prime:

7! + 2 is divisible by 2 (since 2 divides 7! and 2 divides 2)

7! + 3 is divisible by 3 (since 3 divides 7! and 3 divides 3)

7! + 4 is divisible by 4 (since 4 divides 7! and 4 divides 4)

7! + 5 is divisible by 5 (since 5 divides 7! and 5 divides 5)

7! + 6 is divisible by 6 (since 6 divides 7! and 6 divides 6)

7! + 7 is divisible by 7 (since 7 divides 7! and 7 divides 7)

Since each of these numbers is divisible by a number other than 1 and itself, none of these numbers is a prime.

Answer: A

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