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Number S is obtained by squaring the sum of digits of a two

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Number S is obtained by squaring the sum of digits of a two [#permalink] New post 10 Nov 2010, 01:28
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81% (02:36) correct 19% (01:52) wrong based on 57 sessions
Number S is obtained by squaring the sum of digits of a two digit number D. If difference between S and D is 27, then the two digit number D is:

A. 24
B. 54
C. 34
D. 45
E. 25

There is following back-solving method to find an answer:
(b) satisfies the given condition, i.e. (5+4)^2–54=27

(the source: Winners’ Guide to GMAT Math – Part II)

But, can somebody advise me what is a straight-way-solution method, if any?
[Reveal] Spoiler: OA
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Re: sum of digits of a two digit number [#permalink] New post 10 Nov 2010, 08:57
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I did not see anyhting other than backsolving to resolve this problem. Maybe Bunuel knows!!!!
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Re: sum of digits of a two digit number [#permalink] New post 06 Nov 2012, 07:59
D = 10x + y

S = 10x^2 + y^2

S-D --> (10x^2 + y^2) - (10x + y) = 27 --> 10x (x-1) + y (y+1) = 27 ---->>> and then further calculation but I'm stuck here! So I have to agree with maybe Bunuel knowwwsssss!
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Re: Number S is obtained by squaring the sum of digits of a two [#permalink] New post 12 Nov 2013, 11:23
feruz77 wrote:
Number S is obtained by squaring the sum of digits of a two digit number D. If difference between S and D is 27, then the two digit number D is:

A. 24
B. 54
C. 34
D. 45
E. 25

There is following back-solving method to find an answer:
(b) satisfies the given condition, i.e. (5+4)^2–54=27

(the source: Winners’ Guide to GMAT Math – Part II)

But, can somebody advise me what is a straight-way-solution method, if any?


Agree with you guys this one seems a bit tough. Let's hope Bunuel gives us a hand here.

Cheers
J :)
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Re: Number S is obtained by squaring the sum of digits of a two [#permalink] New post 12 Nov 2013, 11:57
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feruz77 wrote:
Number S is obtained by squaring the sum of digits of a two digit number D. If difference between S and D is 27, then the two digit number D is:

A. 24
B. 54
C. 34
D. 45
E. 25


This problem doesn't need a direct method once you realise that S = 27+D
Also, S is a perfect square. Thus, we can eliminate D and E straightaway, as the units digit in both the cases will be 2. Only option B gives a perfect square.
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Re: Number S is obtained by squaring the sum of digits of a two [#permalink] New post 02 Feb 2014, 04:02
feruz77 wrote:
Number S is obtained by squaring the sum of digits of a two digit number D. If difference between S and D is 27, then the two digit number D is:

A. 24
B. 54
C. 34
D. 45
E. 25

There is following back-solving method to find an answer:
(b) satisfies the given condition, i.e. (5+4)^2–54=27

(the source: Winners’ Guide to GMAT Math – Part II)

But, can somebody advise me what is a straight-way-solution method, if any?


Hi Bunuel, could you please solve this problem? Thanks
Re: Number S is obtained by squaring the sum of digits of a two   [#permalink] 02 Feb 2014, 04:02
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Number S is obtained by squaring the sum of digits of a two

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