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19 Jan 2022, 00:19
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D
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Difficulty:
95%
(hard)
Question Stats:
34% (02:26) correct
66%
(02:19)
wrong
based on 71
sessions
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Date
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Not Attempted Yet
If M = 5.abc then what is the value of b + c?
(1) The last two digits of the product of M and 125 is 72.
(2) \(b^2 – c^2\) = 13
(1) The last two digits of the product of M and 125 is 72.
(2) \(b^2 – c^2\) = 13
20 Jan 2022, 00:02
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AbhiroopGhosh
(1) The last two digits of the product of M and 125 is 72.
This means 5.abc * 125 = xy72
\(5.abc*\frac{125*8}{8}=xy72\)..........\(5.abc*\frac{1000}{8}=xy72\)........\(5abc*\frac{1}{8}=xy72\)
5abc=##76.....Thus b=7 and c=6.
b+c=13
Sufficient
(2) \(b^2 – c^2\) = 13
\((b-c)(b+c)=13=1*13\)
b and c are positive, so b+c > b-c.
Hence, b+c = 13
Sufficient
D
20 Jan 2022, 08:37
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AbhiroopGhosh
Statement 1 Alone:
The last two digits of a product are only affected by the two digits in each factor. We will write this as \(0.0bc * 125 \approx 72\), which means the product on the left must end in the digits 72.
This is \(0.0bc * \frac{500}{4} \approx 72\) and \(b.c \approx 72 * \frac{4}{5}\). We can confirm b.c will be related to the last digits of \(72*\frac{4}{5} = 57.6\). Thus we can confirm b.c = 7.6, and statement 1 alone is sufficient.
Statement 2 Alone:
We may rewrite this as \((b + c)(b - c) = 13\). Since the only way to break down 13 is 13 = 13*1, we must have \(b + c = 13\) with \(b - c = 1\). Thus statement 2 alone is sufficient.
Answer: D
