What is the sum of the digits of positive integer q?

Question

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(1) The sum of the digits of q is an element of the set {226, 313, 447, 617}

(2) q = n^3 - n for some positive integer n.

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Archit3110 · Answer

#1
is clearly insufficient
#2
q=n^3-n for some positive integer n.
q=n(n+1)(n-1)
three consective integers , multiple of 3
insufficient
from 1 &2
q= 447
multiple of 3
IMO C

What is the sum of the digits of positive integer q?

(1) The sum of the digits of q is an element of the set \{226,313,447,617\}

(2) q=n^3-n for some positive integer n.

exc4libur · Answer

(1) The sum of the digits of q is an element of the set \{226,313,447,617\}   insufic

(2) q=n^3-n for some positive integer n.   insufic

q=n^3-n=n(n^2-1)=n(n-1)(n+1)…q=(even,mult )

(1)&(2)   sufic

q=multiple(3): sum of its digits must be multiple of 3.
digits(q)=447=15=m(3)

Ans (C)

unraveled · Answer

What is the sum of the digits of positive integer q?

(1) The sum of the digits of q is an element of the set \{226,313,447,617\}
The sum of the digits can be any of the elements of the set given - which one is not known.

INSUFFICIENT.

(2)  q=n^3-n  for some positive integer n.
n can take any value thus q can take any value. Hence no unique sum of digits.

INSUFFICIENT.

Together 1 and 2
As q = (n-1) . n . (n+1) i.e. product of three consecutive numbers but with various possibilities.
Number of digits can vary for a sum of digits.

Thus INSUFFICIENT.

IMO Answer E.

freedom128 · Answer

What is the sum of the digits of positive integer q?

(1) The sum of the digits of q is an element of the set {226,313,447,617}
Clearly NOT SUFFICIENT. We don't know which exact element is the answer.

(2) q=(n-1)n(n+1) for some positive integer n.
q=6,24,60,120,210,504,... with the corresponding sum of the digits of q is: 6,6,6,3,3,9, ..., respectively. We are unable to determine the exact sum of the digits of positive integer q. 
NOT SUFFICIENT.

(1)+(2)
We understand from the patterns observed in (2) that the sum of the digits of positive integer q is DIVISIBLE by 3. From any elements within the set {226,313,447,617}, ONLY 447 is divisible by 3. Thus, the sum of the digits of positive integer q is 447.
SUFFICIENT.

FINAL ANSWER IS (C)

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minustark · Answer

What is the sum of the digits of positive integer q?

(1) The sum of the digits of q is an element of the set \{226,313,447,617\}

(2) q=n^3-n for some positive integer n.

(1) No single sum can be determined from the set. Not sufficient.

(2) q = n (n^2 - 1) = (n -1) n (n+1). Positive integer q can be expressed as the product of 3 consecutive integers. not sufficient.

Together, sum of 3 consecutive integers must be divisible by 3. Among the numbers in the set only 447 fulfills the condition. Sufficient.

Rinng0 · Answer

1) From 1 - Not sufficient
2) From 2 - n^3 - n = n(n^2-1)=n(n+1)(n-1) - Not sufficient

combining 1 & 2, 
n(n-+1)(n-1) - always divisible by 3. 
Among the elements {226,313,447,617} in the set, only 447 divisible by 3.

So, C

lacktutor · Answer

What is the sum of the digits of positive integer q?

(Statement1) The sum of the digits of q is an element of the set {226,313,447,617}
—> No info about exactly what q is. The sum of digits of q could be anything. 
Clearly insufficient.

(Statement2):  q=n^3-n  for some positive integer n. 
q = n(n +1)(n—1) —> q is the product of 3 consecutive positive integers—> q is divisible by 3.

—> if q is divisible by 3, the sum of the digits of q is also divisible by 3. 
q could be 210, 120 and so on. 
Insufficient.

Taken together 1&2: 
—> q is divisible by 3, and the sum of the digits of q is also divisible by 3,—> an element of the set {226,313,447,617}.

—> in the set, only 447 is divisible by 3, —> 4+4+7 = 15 
Sufficient

The answer is C

Good question. Honestly, I got some help with it.

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sanjitscorps18 · Answer

(1) The sum of the digits of q is an element of the set {226, 313, 447, 617}

Any of the 4 numbers could be the answer hence not sufficient

(2) q = n^3 - n for some positive integer n.

=> q = n * (n^2 - 1) = (n-1) * n * (n+1)
This suggests that q is a product of 3 consecutive numbers and hence even

Statement (1) and (2) combined we get.

Only 226 is an even number hence that's the answer.

Option C

What is the sum of the digits of positive integer q?

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