The number 152 is equal to the sum of the cubes of two integ

Oldest

Best Reply

Author

Message

TAGS:

Manager

Joined: 24 Jan 2013

Posts: 76

Followers: 3

Kudos [?]: 27 [0], given: 6

The number 152 is equal to the sum of the cubes of two integ [#permalink]

26 Feb 2013, 17:33

00:00

Question Stats:

85% (01:47) correct

14% (01:28) wrong

based on 5 sessions

The number 152 is equal to the sum of the cubes of two integers. What is the product of those integers?

A) 8
B) 15
C) 21
D) 27
E) 39

[Reveal] Spoiler: Solution

Do not try to do it using the decomposition in factors: that would be a non-sense, as you are told that 152=X^3+Y^3 (and not X^3*Y^3). Just do the cube of the first integers: 1^3=1 ------> 2^3=8 ------> 3^3=27 ------> 4^3=84 ------> 5^3=125 ------> when reaching this point, we can see that 125+27=152. Therefore, X=3 and Y=5. And the product of X*Y=15. Solution B.

[Reveal] Spoiler: OA

_________________

Does this post deserve KUDOS?

Free Prep: Self-prepare GMAT for free and GMAT Math tips for free
Free Flashcards: Free GMAT Flashcards

More: "All I wish someone had told me about GMAT beforehand"
There are many things you want to know before doing the GMAT exam (how is exam day, what to expect, how to think, to do's...), and you have them in this blog, in a simple way

GMAT Club team member

Joined: 02 Sep 2009

Posts: 11506

Followers: 1790

Kudos [?]: 9513 [1] , given: 826

Re: The number 152 is equal to the sum of the cubes of two integ [#permalink]

27 Feb 2013, 02:06

This post received
KUDOS

johnwesley wrote:

The number 152 is equal to the sum of the cubes of two integers. What is the product of those integers?

A) 8
B) 15
C) 21
D) 27
E) 39

Do not try to do it using the decomposition in factors: that would be a non-sense, as you are told that 152=X^3+Y^3 (and not X^3*Y^3). Just do the cube of the first integers: 1^3=1 ------> 2^3=8 ------> 3^3=27 ------> 4^3=84 ------> 5^3=125 ------> when reaching this point, we can see that 125+27=152. Therefore, X=3 and Y=5. And the product of X*Y=15. Solution B.]

Apart from 3 and 4, -4 and 6 also satisfy the given condition: (-4)^3 + 6^3 =152, so the product could also be -4*6 = -24.
_________________

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!

What are GMAT Club Tests?
25 extra-hard Quant Tests

Find out what's new at GMAT Club - latest features and updates

Manager

Joined: 24 Jan 2013

Posts: 76

Followers: 3

Kudos [?]: 27 [0], given: 6

Re: The number 152 is equal to the sum of the cubes of two integ [#permalink]

27 Feb 2013, 13:29

Of course, but as that answer is not included in the options... better put answer is 3 and 5, therefore 3*5=15. Solution B. :wink:

_________________

GMAT Club team member

Joined: 02 Sep 2009

Posts: 11506

Followers: 1790

Kudos [?]: 9513 [0], given: 826

Re: The number 152 is equal to the sum of the cubes of two integ [#permalink]

27 Feb 2013, 15:30

johnwesley wrote:

Of course, but as that answer is not included in the options... better put answer is 3 and 5, therefore 3*5=15. Solution B. :wink:

I know that, thank you. The point is that it would be better if it were mentioned that x and y are positive integers.
_________________

Veritas Prep GMAT Instructor

Joined: 16 Oct 2010

Posts: 3104

Location: Pune, India

Followers: 567

Kudos [?]: 1992 [0], given: 92

Re: The number 152 is equal to the sum of the cubes of two integ [#permalink]

27 Feb 2013, 21:26

johnwesley wrote:

Actually, decomposition into factors can easily give you the answer here. You should just do the decomposition of the right thing i.e. the options since they represent the product of those integers.

Since the sum of cubes is 152, the numbers cannot be larger than 5 since 6^3 itself is 216.

21, 27, 39 - The factors are too large so ignore

8 - (2, 4) Does not satisfy

15 - (3, 5) Yes. 3^3 + 5^3 = 152 - Answer
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save 10% on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Intern

Joined: 15 Mar 2012

Posts: 40

Location: United States

Concentration: Marketing, Strategy

Schools: Ross '15, Tuck '16, Duke '16, ESADE '15

Followers: 0

Kudos [?]: 6 [0], given: 12

Re: The number 152 is equal to the sum of the cubes of two integ [#permalink]

28 Feb 2013, 14:21

VeritasPrepKarishma wrote:

johnwesley wrote:

You nailed it Karishma, that was exactly my approach.
Since 6^3 surpasses 152, I sticked with an answer choice that had a factor of <6. Then with a little math I discarded 8, having 15 alone as my answer choice.
_________________

MV
"Better to fight for something than live for nothing.” ― George S. Patton Jr

Re: The number 152 is equal to the sum of the cubes of two integ [#permalink] 28 Feb 2013, 14:21

		Similar topics	Author	Replies	Last post
Similar Topics:		The sum of cubes of first five whole numbers	stolyar	8	20 Jul 2003, 01:15
		What positive number, when squared, is equal to the cube of	scoobee	4	12 Oct 2004, 13:23
	1	Sum of two numbers	mdfrahim	2	12 Jun 2009, 12:37
		The sum of the digits of a two digit number..	vomhorizon	4	14 Nov 2012, 08:34
	1	A cube is made up of equal smaller cubes. Two of the sides	SravnaTestPrep	2	19 Mar 2013, 23:17

The number 152 is equal to the sum of the cubes of two integ

Main navigation

GMAT Resources

Partners

MBA Resources

GMAT ® is a registered trademark of the Graduate Management Admission Council ® (GMAC ®). GMAT Club's website has not been reviewed or endorsed by GMAC.