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

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Math Expert
Joined: 02 Sep 2009
Posts: 43789
Let a and b be digits. What is the sum b.aaa + a.bbb? [#permalink]

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10 Jan 2017, 03:03
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59% (00:51) correct 41% (00:52) wrong based on 91 sessions

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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
[Reveal] Spoiler: OA

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Posts: 367
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Re: Let a and b be digits. What is the sum b.aaa + a.bbb? [#permalink]

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10 Jan 2017, 05:34
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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]

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10 Jan 2017, 23:20
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]

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22 Jan 2018, 05:15
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Re: Let a and b be digits. What is the sum b.aaa + a.bbb?   [#permalink] 22 Jan 2018, 05:15
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