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

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

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26 Feb 2013, 17:33
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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
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Re: The number 152 is equal to the sum of the cubes of two integ [#permalink]

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27 Feb 2013, 02:06
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Expert's post
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.
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Re: The number 152 is equal to the sum of the cubes of two integ [#permalink]

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27 Feb 2013, 13:29
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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.
Math Expert
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Kudos [?]: 79463 [1] , given: 10018

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

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27 Feb 2013, 15:30
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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.

I know that, thank you. The point is that it would be better if it were mentioned that x and y are positive integers.
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Re: The number 152 is equal to the sum of the cubes of two integ [#permalink]

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27 Feb 2013, 21:26
2
KUDOS
Expert's post
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.

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

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28 Feb 2013, 14:21
VeritasPrepKarishma wrote:
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.

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

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

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19 Jul 2014, 05:13
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Re: The number 152 is equal to the sum of the cubes of two integ   [#permalink] 19 Jul 2014, 05:13
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