1575 Ã— k is a perfect square

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Tue Sep 14, 2010 4:35 am

What is the smallest positive integer k such that the product 1575 Ã— k is a perfect square?
(A) 7
(B) 9
(C) 15
(D) 25
(E) 63

[spoiler]Source: https://readyforgmat.com[/spoiler]

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Source: Beat The GMAT — Problem Solving | Tue Sep 14, 2010 4:35 am

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

by Rahul@gurome » Tue Sep 14, 2010 4:42 am

1575 = 3^2 * 5^2 * 7
So, if k = 7 (which is the smallest positive integer), then 1575 Ã— 7 = 3^2 * 5^2 * 7^2, which will be a perfect square.

The correct answer is [spoiler](A)[/spoiler].

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Tue Sep 14, 2010 4:50 am

Rahul@gurome wrote:1575 = 3^2 * 5^2 * 7
So, if k = 7 (which is the smallest positive integer), then 1575 Ã— 7 = 3^2 * 5^2 * 7^2, which will be a perfect square.

The correct answer is [spoiler](A)[/spoiler].

Good! Generally, on GMAT PS, the smallest hardly happens to be the smallest of all the choices, this question is just an EXCEPTION, isn't it, Rahul?

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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GMAT/MBA Expert

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

by Rahul@gurome » Tue Sep 14, 2010 4:54 am

sanju09 wrote: Good! Generally, on GMAT PS, the smallest hardly happens to be the smallest of all the choices, this question is just an EXCEPTION, isn't it, Rahul?

Right Sanju, I agree with you.

Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)

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