How should I read this number?

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

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

Pugalenthi: Junior | Next Rank: 30 Posts; Posts: 29; Joined: Fri Sep 25, 2009 9:26 am

How should I read this number?

by Pugalenthi » Fri May 11, 2012 10:22 am

If 5,400n is the square of an integer, what is the smallest possible integer value of n?
(A) 2
(B) 3
(C) 5
(D) 6
(E) 15

How should I read 5,400n? I know that I should use prime factorization to solve this problem. My struggle is...should I apply the logic to 5400 or 5400(2/3/5/6/15)? Any pointers would be much appreciated.

Quote

Source: Beat The GMAT — Problem Solving | Fri May 11, 2012 10:22 am

LalaB: Master | Next Rank: 500 Posts; Posts: 425; Joined: Wed Dec 08, 2010 9:00 am; Thanked: 56 times; Followed by:7 members; GMAT Score:690

by LalaB » Fri May 11, 2012 10:48 am

54*100=6*9*4*25=3^3*2^3*5^2

3^3*2^3*5^2*n=(some integer)^2

so, n =3*2=6

Happy are those who dream dreams and are ready to pay the price to make them come true.(c)

In order to succeed, your desire for success should be greater than your fear of failure.(c)

Quote

African Dude: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Tue Jan 10, 2012 5:44 am; Thanked: 2 times

by African Dude » Fri May 11, 2012 10:51 am

Pugalenthi wrote:If 5,400n is the square of an integer, what is the smallest possible integer value of n?
(A) 2
(B) 3
(C) 5
(D) 6
(E) 15

How should I read 5,400n? I know that I should use prime factorization to solve this problem. My struggle is...should I apply the logic to 5400 or 5400(2/3/5/6/15)? Any pointers would be much appreciated.

The 1st thing you need to remember is that a perfect square contains only even powers. Start by factorising the number given:
=54(100)
=9x6x10x10
=3x3x3x2x2x5x2x5
2^3 x 3^3x 5^2

Notice that the powers of 2 and 3 are odd implying that 5400 is not a square. 5400 x n must yield in a prime factorisation with all even powers. This therefore means that n must have at least one 2 and one 3 to make it: 2^4 x 3^4 x 5^2. Hence n can only be 2 x 3 = 6 ----choose D

Quote

Pugalenthi: Junior | Next Rank: 30 Posts; Posts: 29; Joined: Fri Sep 25, 2009 9:26 am

by Pugalenthi » Fri May 11, 2012 11:57 am

Thank you for your reply and I understand the logic but my question is this....5400n ..given this number...why split this as 54*100 ? Why it shouldn't be 54002?