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26 Feb 2013, 17:33
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
79% (01:37) correct
21%
(02:01)
wrong
based on 431
sessions
History
Date
Time
Result
Not Attempted Yet
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
A) 8
B) 15
C) 21
D) 27
E) 39
Show SpoilerSolution
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.
27 Feb 2013, 15:30
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johnwesley
I know that, thank you. The point is that it would be better if it were mentioned that x and y are positive integers.
27 Feb 2013, 21:26
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johnwesley
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
