Question on Perfect Square 8

Expert replies

richachampion: Legendary Member; Posts: 698; Joined: Tue Jul 21, 2015 12:12 amFollowed by: 26 members; Location: Noida, India; Thanked: 32 times; GMAT Score:740

by richachampion » Mon Oct 17, 2016 3:16 am

For any even integer P, 300 multiplied by P is square of an integer. What is the least value of P?

A) 3
B) 4
C) 10
D) 12
E) 14

OA: D

R I C H A,
My GMAT Journey: 470 â†’ 720 â†’ 740
Target Score: 760+
[email protected]
1. Press thanks if you like my solution.
2. Contact me if you are not improving. (No Free Lunch!)

Like this post

Source: Beat The GMAT — Problem Solving | Mon Oct 17, 2016 3:16 am

richachampion: Legendary Member; Posts: 698; Joined: Tue Jul 21, 2015 12:12 amFollowed by: 26 members; Location: Noida, India; Thanked: 32 times; GMAT Score:740

by richachampion » Mon Oct 17, 2016 3:16 am

Not a tough question, but question stem is slightly Tricky.

R I C H A,
My GMAT Journey: 470 â†’ 720 â†’ 740
Target Score: 760+
[email protected]
1. Press thanks if you like my solution.
2. Contact me if you are not improving. (No Free Lunch!)

Like this post

fiza gupta: Master | Next Rank: 500 Posts; Posts: 216; Joined: Sun Jul 31, 2016 9:55 pmFollowed by: 7 members; Location: Punjab; Thanked: 31 times

by fiza gupta » Mon Oct 17, 2016 5:51 am

300*p(even integer) = perfect square
let y = 100*3*P
100 is a perfect square but not 3
to make y a perfect square P should be 3 or a multiple of 3
p=3 or p =3*z(z a perfect square)(3*4,3*9.....)
but p is even so
p = 3*4(12),3*16(48)...........

only option D satisfies

Fiza Gupta

Like this post

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Mon Oct 17, 2016 10:16 am

Hi richachampion,

This question is based on the same concept as the other prime-factor questions that you posted: when you prime-factor a perfect square, each of the prime factors MUST show up an EVEN number of times...

eg. 9 = (3)(3) here, there are TWO 3s.
eg. 100 = (2)(2)(5)(5) here, there are TWO 2s and TWO 5s
eg. 16 = (2)(2)(2)(2) = here, there are FOUR 2s
Etc.

We're told that P is an EVEN INTEGER and that (300)(P) is a PERFECT SQUARE. We have to be careful to incorporate ALL of the information that we're given.. Prime-factoring this number will get us...

(300)(P) =
(10)(30)(P) =
(2)(5)(2)(3)(5)(P) =
(2)(2)(3)(5)(5)(P)

We have TWO 2s and TWO 5s, but only ONE 3. We need there to be an even number of each prime factor. At first glance, you might think that P must equal 3... However, 3 is NOT an EVEN INTEGER. So we need P to contain a '3' AND and at least TWO 2s (so that P will be EVEN).

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Like this post

Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Fri Oct 28, 2016 12:42 am

The OA (and the explanations above) are not quite correct.

Let's set p = 2k, where k is some unknown integer.

300 * p = a square

300 * 2k = a square

600k = a square

(100) * 6k = a square

Since 100 is a square, 6k must also be a square. If k = 0, then 6k is a square, and we're set. Any k < 0 won't work, since squares are nonnegative.

Since p = 2k, p = 0 is our smallest solution, and we're done!

(Unfortunately, whoever wrote this question forgot to put the correct answer. :/ But if we want p > 0, you can see that the next 6k that is a square is 6*6, which gives k = 6 and p = 2*k = 2*6 = 12.)

Save $100 on any VP online course!

Like this post

Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Fri Oct 28, 2016 12:46 am

richachampion wrote:Not a tough question, but question stem is slightly Tricky.

Beware!

The question was subtle enough to fool whoever wrote it (p = 0 is an annoying detail, but exactly the sort of annoying detail that the GMAT likes to test!) ... on the GMAT, if it seems easy, be very suspicious!

Save $100 on any VP online course!

Like this post

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8138; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Mon Oct 31, 2016 10:32 am

richachampion wrote:For any even integer P, 300 multiplied by P is square of an integer. What is the least value of P?

A) 3
B) 4
C) 10
D) 12
E) 14

OA: D

If 300P is a perfect square, then its prime factorization must contain only even exponents. Let's begin by prime factoring 300.

300 = 30 x 10 = 5 x 6 x 5 x 2 = 5 x 3 x 2 x 5 x 2 = 5^2 x 3^1 x 2^2

We can see that 300 is not a perfect square because its prime factorization contains an odd exponent (that is, 3^1). This means that P must contribute the missing factor. However, we are given that P must also be an even integer. Thus, in order to keep "an even number" of twos, P must be divisible by 2^2. Thus P must be divisible by 3^1 x 2^2 = 12. Since we want the least value of P, P must be 12.

In fact, if P = 12, then 300P = 5^2 x 3^2 x 2^4, which is a perfect square.

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review