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16 Apr 2020, 09:34
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D
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Difficulty:
55%
(hard)
Question Stats:
71% (02:58) correct
29%
(02:43)
wrong
based on 147
sessions
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Not Attempted Yet
In a finite list of positive integers, each number, except for the last number, is a proper divisor of the next number in the list. If the first number in the list is 1 and the last is 650, what is the greatest possible sum of the numbers in the list?
(A) 753
(B) 892
(C) 934
(D) 1054
(E) 1128
(A) 753
(B) 892
(C) 934
(D) 1054
(E) 1128
GraemeGmatPanda
Joined: 13 Apr 2020
Last visit: 21 Apr 2026
Posts: 102
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Location: United Kingdom
Concentration: Marketing
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16 Apr 2020, 09:46
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Nice question Ravixxx
Prime breakdown of 650 is \(2, 5^2, 13\)
Starting from the end of the list (650) and working backwards, the highest proper divisor of 650 is 5^2x13 = 325
The next one will be 5x13 = 65
The next one will be 13, which is prime hence we get to the end of the list (with 1 at the end)
Adding them all up, we get to (D) 1,054
Prime breakdown of 650 is \(2, 5^2, 13\)
Starting from the end of the list (650) and working backwards, the highest proper divisor of 650 is 5^2x13 = 325
The next one will be 5x13 = 65
The next one will be 13, which is prime hence we get to the end of the list (with 1 at the end)
Adding them all up, we get to (D) 1,054
16 Apr 2020, 10:20
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Ravixxx
The list starts from 1 and ends at 650, for each term as we progress we will add one more factor and eventually hit 650. 650 = 65*10 = 13*5*5*2.
There are many ways to achieve this, we can multiply by 2, then 5, then 5, then 13 and that works our way towards 650. We could arrange the factors in any order but the question wants us to find the arrangement that produces the greatest sum.
To do that, we need to start by feeding the big factors first which will let us approach 650 faster. Then the list would be {1, 13, 65, 325, 650}. This adds up to 1054, which is answer D.
If in doubt that this is the best arrangement, we can always try the other extreme option, which is to multiply smaller factors first. This gives us {1, 2, 10, 50, 650} and we can visually see the numbers are much smaller.
Ans: D
