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# Let a, b, c be distinct digits. Consider a two digit number 'ab' and

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Math Expert
Joined: 02 Sep 2009
Posts: 64249
Let a, b, c be distinct digits. Consider a two digit number 'ab' and  [#permalink]

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02 Apr 2020, 03:12
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Difficulty:

45% (medium)

Question Stats:

67% (01:55) correct 33% (01:45) wrong based on 21 sessions

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Let a, b, c be distinct digits. Consider a two digit number 'ab' and a three digit number 'ccb'. If (ab)^2 = ccb and ccb > 300 then the value of b is

A. 0
B. 1
C. 5
D. 6
E. 7

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Joined: 07 May 2019
Posts: 709
Location: India
Re: Let a, b, c be distinct digits. Consider a two digit number 'ab' and  [#permalink]

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02 Apr 2020, 05:58
1
Bunuel wrote:
Let a, b, c be distinct digits. Consider a two digit number 'ab' and a three digit number 'ccb'. If (ab)^2 = ccb and ccb > 300 then the value of b is

A. 0
B. 1
C. 5
D. 6
E. 7

Solution:

o a, b, and c are distinct integers.
o $$ab^2 = ccb$$, ccb>300
o What does it mean?
o It means ccb is a perfect square of a 2-digit number which is greater than 300.
 $$300 < ccb < 999$$ [ccb is a 3-digit number]
 $$17^2<ccb < 31^2$$
 $$17 < ab < 31$$
o The value of ab is that number whose unit digit is equal to the unit digit of square of that number
 Possible values of ab are 21, 25, and 26
 Possible values of $$ab^2$$ are 441, 625, and 676
• The only value which satisfy ccb is $$441$$
• Thus $$b = 1$$.
Hence, the correct answer is Option B.
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Re: Let a, b, c be distinct digits. Consider a two digit number 'ab' and   [#permalink] 02 Apr 2020, 05:58