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mtouchton
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John Bob wants to leave behind his life-time savings of s dollars... Updated on: 17 Dec 2019, 11:25
Originally posted by mtouchton on 17 Dec 2019, 10:25.
Last edited by mtouchton on 17 Dec 2019, 11:25, edited 1 time in total.
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75% (hard)

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55% (02:00) correct 45% (01:54) wrong based on 125 sessions

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John Bob wants to leave behind his life-time savings of s dollars to his c children, where s and c are positive integers. Given that each dollar equals 100 cents, and one cent is the smallest unit of currency that John Bob can leave behind for any of his children, can John Bob divide his savings equally between his children?

(1) 1 < c < 8 and c is a power of 2 (c =\(2^k\) for some integer k)

(2) 31 < s < 43

Hi all, I'm looking for help to solve this.
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Raxit85
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John Bob wants to leave behind his life-time savings of s dollars... 17 Dec 2019, 10:43
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Hi, mtouchton,

Can you please confirm that c=\(2^k\) condition, whether is it absolute mod symbol?

Regards

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mtouchton
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John Bob wants to leave behind his life-time savings of s dollars... 17 Dec 2019, 11:28
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Sorry about that, Raxit85. I've fixed the code. Let me know if it's clear for you now.

Thanks!
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John Bob wants to leave behind his life-time savings of s dollars... 17 Dec 2019, 14:36
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mtouchton
John Bob wants to leave behind his life-time savings of s dollars to his c children, where s and c are positive integers. Given that each dollar equals 100 cents, and one cent is the smallest unit of currency that John Bob can leave behind for any of his children, can John Bob divide his savings equally between his children?

(1) 1 < c < 8 and c is a power of 2 (c =\(2^k\) for some integer k)

(2) 31 < s < 43

Hi all, I'm looking for help to solve this.
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Interesting problem. It's a little bit wordier, for a divisibility problem, than you'd normally see, but it also has kind of a clever trick to it!

JB has a round number of dollars (presumably - this problem should have clearly stated that s is an integer, but let's assume that's what the writer intended.) Since he has s dollars, he has 100s cents. These 100s cents can only be divided among his children if 100s is evenly divisible by c. So, rephrase the question: is 100s divisible by c?

Statement 1: This is a complicated way of saying that c equals either 2 or 4, since those are the only powers of 2 that are between 1 and 8. If c = 2, then 100s/c = 100s/2 = 50s, which is an integer number of cents, so the answer to the question is 'yes'.

If c = 4, the situation is similar. 100s/c = 100s/4 = 25s, which is an integer number of cents, and the answer is "yes" again. So, statement 1 is sufficient.

Statement 2: JB has between 31 and 43 dollars, exclusive. To show that this is insufficient, we should come up with one scenario where his money can't be divided among his (unknown number of) children, and one scenario where it can.

For instance, suppose he has 32 dollars. If he has 7 children (c = 7), then the money can't be evenly divided, since 3200 isn't divisible by 7. But if he has 2 children (c = 2), then the money can be evenly divided, with 16 dollars (1600 cents) going to each child. Since the answer might be yes or no, the statement is insufficient.

So, the answer to the problem is A.
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John Bob wants to leave behind his life-time savings of s dollars... 17 Dec 2019, 14:50
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Thank you, ccooley! That's very helpful.
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John Bob wants to leave behind his life-time savings of s dollars... 27 Feb 2026, 08:55
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