BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Book got this problem wrong

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 41
Joined: Sat Mar 09, 2013 1:10 pm
Thanked: 1 times

Book got this problem wrong

by Rudy414 » Fri Mar 22, 2013 2:53 pm
If x is even, and 90 (less than/equal to) x (less than/equal to) 100, what is the value of x?

1) x and x/2 have the same distinct prime factors

2) x/2 has two prime factors

The answer key says, and I quote verbatim, "...Statement 1 is not sufficient. Eliminate choices B, C, and E." And it says the answer is C. Clearly, something is wrong here.
Top
Source: — Data Sufficiency |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 511
Joined: Wed Aug 11, 2010 9:47 am
Location: Delhi, India
Thanked: 344 times
Followed by:86 members

by Anju@Gurome » Fri Mar 22, 2013 3:05 pm
Rudy414 wrote:If x is even, and 90 ≤ x ≤ 100, what is the value of x?

1) x and x/2 have the same distinct prime factors
2) x/2 has two prime factors
Possible values of x are : 90, 92, 94, 96, 98, and 100

Statement 1: This means x must be divisible by 4
Hence, possible values of x are : 92, 96, and 100

Not sufficient

Statement 2: Possible values of x/2 are : 45, 46, 47, 48, 49, and 50
Now,
  • 45 = 3*3*5
    46 = 2*23
    47 = 47
    48 = 2*2*2*2*3
    49 = 7*7
    50 = 2*5*5
As x/2 has two prime factors, possible values of x/2 are : 46 and 49
Hence, possible values of x are : 92 and 98

Not sufficient

1 & 2 Together: Only possible value of x is 92

Sufficient

The correct answer is C.
Anju Agarwal
Quant Expert, Gurome

Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.

§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §
Top
Senior | Next Rank: 100 Posts
Posts: 41
Joined: Sat Mar 09, 2013 1:10 pm
Thanked: 1 times

by Rudy414 » Sat Mar 23, 2013 5:42 am
For statement 1, can you explain why x must be divisible by 4? I don't quite understand how you reached that conclusion.
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 511
Joined: Wed Aug 11, 2010 9:47 am
Location: Delhi, India
Thanked: 344 times
Followed by:86 members

by Anju@Gurome » Sat Mar 23, 2013 6:03 am
Rudy414 wrote:For statement 1, can you explain why x must be divisible by 4? I don't quite understand how you reached that conclusion.
As x is even, let us assume that x = 2*a*b*c*..., where a, b, c etc are prime factors of x.
So, x/2 = a*b*c*...

As x and x/2 have same distinct prime factors and 2 is a prime factor of x, 2 must be a prime factor of x/2 also. Hence, at least one of a, b, c etc must be equal to 2. Which in turn means x will be divisible by another 2, i.e. x is divisible by 4.

Hope that helps.
Anju Agarwal
Quant Expert, Gurome

Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.

§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §
Top
Post new topic Post Reply
• Page 1 of 1