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Let a and b be digits. What is the sum b.aaa + a.bbb?

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Bunuel
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Let a and b be digits. What is the sum b.aaa + a.bbb? [#permalink] New post  10 Jan 2017, 04:03
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Let a and b be digits. What is the sum b.aaa + a.bbb?

(1) a + b = 10
(2) a = b
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Re: Let a and b be digits. What is the sum b.aaa + a.bbb? [#permalink] New post  10 Jan 2017, 06:34
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Bunuel wrote:
Let a and b be digits. What is the sum b.aaa + a.bbb?

(1) a + b = 10
(2) a = b


\(b.aaa + a.bbb = \frac{baaa}{1000} + \frac{abbb}{1000} = \frac{1000b + 100a + 10 a + a + 1000a + 100b + 10b + b}{1000} = \\
\\
= a+b + \frac{a + b}{10} + \frac{a + b}{100} + \frac{a + b}{1000}\)

(1) a + b = 10

10 + 1 + 0.1 + 0.01 = 11.11 Sufficient.

(2) a = b

\(2a + \frac{2a}{10} + \frac{2a}{100} + \frac{2a}{1000}\). No information about a or b (1.111 + 1.111 or 2.222 + 2.222 etc.). Insufficient.

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Re: Let a and b be digits. What is the sum b.aaa + a.bbb? [#permalink] New post  11 Jan 2017, 00:20
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Bunuel wrote:
Let a and b be digits. What is the sum b.aaa + a.bbb?

(1) a + b = 10
(2) a = b


Digits are from 0 to 9.

As per statement 1:

a + b = 10

various combinations are 1+9, 2+8, 3+6 etc.
So if a = 1 and b = 9 we have 1.999 + 9.111 = 11.11
a = 2 and b = 8 we have 2.888 + 8.222 = 11.11 etc (various combinations gives the same value . Sufficient

As per statement 2:

a = b

There may various combinations that will yield different sums of a & b
1.111 + 1.111 = 2.222
2.222 + 2.222 = 4.444

Not Sufficient.

(A)
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Re: Let a and b be digits. What is the sum b.aaa + a.bbb? [#permalink] New post  06 May 2019, 06:35
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Re: Let a and b be digits. What is the sum b.aaa + a.bbb? [#permalink]
06 May 2019, 06:35
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