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

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Manager
Joined: 08 Oct 2010
Posts: 212

Kudos [?]: 871 [0], given: 974

Location: Uzbekistan
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WE 3: 10
Number S is obtained by squaring the sum of digits of a two [#permalink]

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10 Nov 2010, 01:28
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Difficulty:

15% (low)

Question Stats:

81% (01:59) correct 19% (01:50) wrong based on 128 sessions

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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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Manager
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Location: Zürich, Switzerland
Re: sum of digits of a two digit number [#permalink]

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10 Nov 2010, 08:57
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I did not see anyhting other than backsolving to resolve this problem. Maybe Bunuel knows!!!!

Kudos [?]: 52 [1], given: 20

Intern
Joined: 02 Nov 2012
Posts: 34

Kudos [?]: 4 [0], given: 11

Re: sum of digits of a two digit number [#permalink]

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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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Current Student
Joined: 06 Sep 2013
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Re: Number S is obtained by squaring the sum of digits of a two [#permalink]

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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

Kudos [?]: 759 [0], given: 355

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Re: Number S is obtained by squaring the sum of digits of a two [#permalink]

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12 Nov 2013, 11:57
3
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2
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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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Intern
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Re: Number S is obtained by squaring the sum of digits of a two [#permalink]

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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

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Re: Number S is obtained by squaring the sum of digits of a two [#permalink]

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25 Feb 2016, 11:28
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Re: Number S is obtained by squaring the sum of digits of a two   [#permalink] 25 Feb 2016, 11:28
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