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Is the three-digit number n less than 550?

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Is the three-digit number n less than 550? [#permalink] New post 15 Jun 2012, 06:34
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Is the three-digit number n less than 550?

(1) The product of the digits in n is 30.
(2) The sum of the digits in n is 10.
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Re: Is the three-digit number n less than 550? [#permalink] New post 15 Jun 2012, 06:39
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Is the three-digit number n less than 550?

(1) The product of the digits in n is 30 --> 30=1*2*3*5 --> n can be any combination of digits from the following two sets: {1, 6(=2*3), 5} or {2, 3, 5}. n can be lees than 550 (eg. 165, 156, ...) OR more than 550 (eg 615, 651). Not sufficient.

(2) The sum of the digits in n is 10 --> Clearly not sufficient. Many combinations are possible 109, 901, ....

(1)+(2) We have the set {2, 3, 5} (as only in this set the sum of the digits is 10). From this set we can not form three digit number more than 550 (max=532). Sufficient.

Answer: C.
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Re: Is the three-digit number n less than 550? [#permalink] New post 25 Jan 2013, 03:37
Bunuel wrote:
Is the three-digit number n less than 550?

(1) The product of the digits in n is 30 --> 30=1*2*3*5 --> n can be any combination of digits from the following two sets: {1, 6(=2*3), 5} or {2, 3, 5}. n can be lees than 550 (eg. 165, 156, ...) OR more than 550 (eg 615, 651). Not sufficient.

(2) The sum of the digits in n is 10 --> Clearly not sufficient. Many combinations are possible 109, 901, ....

(1)+(2) We have the set {2, 3, 5} (as only in this set the sum of the digits is 10). From this set we can not form three digit number more than 550 (max=532). Sufficient.

Answer: C.


i was thinkin terms of prime numbers and so did not think of 1.

how do we avoid this kinda trap?
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Re: Is the three-digit number n less than 550?   [#permalink] 25 Jan 2013, 03:37
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