confused!

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mehaksal: Master | Next Rank: 500 Posts; Posts: 122; Joined: Tue Jul 10, 2012 9:12 amFollowed by: 8 members; Thanked: 2 times

by mehaksal » Sat Aug 25, 2012 4:56 am

If y â‰ 3 and 2x/y is a prime integer greater than 2, which of the following must be true?
I. x = y
II. y = 1
III. x and y are prime integers.
(A) None (B) I only (C) II only (D) III only (E) I and II

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Source: Beat The GMAT — Problem Solving | Sat Aug 25, 2012 4:56 am

vk_vinayak: Legendary Member; Posts: 502; Joined: Tue Jun 03, 2008 11:36 pmFollowed by: 21 members; Thanked: 99 times

by vk_vinayak » Sat Aug 25, 2012 5:12 am

mehaksal wrote:If y â‰ 3 and 2x/y is a prime integer greater than 2, which of the following must be true?
I. x = y
II. y = 1
III. x and y are prime integers.
(A) None (B) I only (C) II only (D) III only (E) I and II

2x/y is a prime integer greater than 2 => 2x/y is an odd integer.

Any prime number greater than 2 is an odd integer.

I). If x=y, then 2x/y becomes 2. FALSE
II) If y=1, then 2X needs to be prime integer, which is never possible. FALSE
III) If x and Y are prime integers, then x/y is not an integer. Therefore, for 2x/y to be an integer, y must be 2, and x must be a prime integer greater than 2. TRUE

Eg: 2 * 17/2 = 17 or 2*3/2 = 3.

Ans: D

- VK

I will (Learn. Recognize. Apply)

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neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Sat Aug 25, 2012 5:37 am

Since, VK already proved that statement I and II are not must-be-true statements, I will show you how statement III is also not a must-be-true condition.

If y â‰ 3 and 2x/y is a prime integer greater than 2, which of the following must be true?
III. x and y are prime integers.

If x = 17 and y = 2 then 2x/y = 17 (A prime number greater than 2) and x,y are prime numbers.
If x = 14 and y = 4 then 2x/y = 28/4 = 7 (A prime number greater than 2) and x,y are NOT prime numbers. Hence, statement III is also not a must-be-true condition.

So, the answer to this question should be A and not D

Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
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mehaksal: Master | Next Rank: 500 Posts; Posts: 122; Joined: Tue Jul 10, 2012 9:12 amFollowed by: 8 members; Thanked: 2 times

by mehaksal » Sun Aug 26, 2012 8:48 pm

neelgandham...very well pointed out...but I generally tend to ignore such cases

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