integer factor of x

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kushal.adhia: Senior | Next Rank: 100 Posts; Posts: 80; Joined: Thu Aug 12, 2010 11:47 pm; Location: chennai, india; Thanked: 2 times

integer factor of x

by kushal.adhia » Wed Oct 20, 2010 2:24 am

If x is a positive integer greater than 1, does x have any integer factor n such that 1 < n < x?

(1) x is even.

(2) 47 < x < 53

OA is B

Can someone help me out with this please??

Kushal

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Source: Beat The GMAT — Data Sufficiency | Wed Oct 20, 2010 2:24 am

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pm; Location: Milpitas, CA; Thanked: 447 times; Followed by:88 members

by Rahul@gurome » Wed Oct 20, 2010 3:37 am

kushal.adhia wrote:If x is a positive integer greater than 1, does x have any integer factor n such that 1 < n < x?

(1) x is even.

(2) 47 < x < 53

OA is B

Can someone help me out with this please??

Kushal

(1) If x is even, x can be equal to 2. 2 has only two integer factors 1 and 2. Thus there is no integer factor n of 2, such that 1 < n < 2.

Not SUFFICIENT.

(2) If 47 < x < 53, x can have the values 48, 49, 50, 51 and 52.

48 = 2*2*2*2*3
49 = 7*7
50 = 2*5*5
51 = 3*17
52 = 2*2*13

Therefore in each of these 5 cases the x have integer factors n (= 2 0r 3 or 5 or 7 etc or their multiples in some cases) such that 1 < n < x.

SUFFICIENT.

The correct answer is B.

Rahul Lakhani
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Gurome, Inc.
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kushal.adhia: Senior | Next Rank: 100 Posts; Posts: 80; Joined: Thu Aug 12, 2010 11:47 pm; Location: chennai, india; Thanked: 2 times