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(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 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.

(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 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.

Excellent Bunuel. I missed the factor "1" when checking the factors of "30". And if you miss this "1" as the factor the answer you end up with is "A", which indeed is wrong.

sm ppl missed "1" as one of the factors , don't think of factorising the thing , think how many ways u can get to 30 using three numbers., u won;t miss 1 thn ..
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We know n <550 (1) Product of the digits = 30 (2) Sum of the digits = 10

(1) alone is insufficient as there are numerous iterations of this that would work: 352, 532, 253, 235, 156, 516, etc. (2) alone is insufficient as there are numerous iterations that would work as well: 352, 235, 235, 163, 127, etc.

Together we can eliminate it down but are still left with a number of solutions: 352, 325, 235, 253, 532, and 523. These all meet both one and two therefore it is C.

Last edited by u0422811 on 17 Sep 2010, 12:17, edited 1 time in total.

Statement 1 and 2 together Case 1: 235 -> 2*3*5 = 30 and 2+3+5 = 10 and also give only one answer 235 < 550. Case 2: 253 -> 2*3*5 = 30 and 2+3+5 = 10 and also give only one answer 253 < 550. Case 3: 325 -> 2*3*5 = 30 and 2+3+5 = 10 and also give only one answer 325 < 550. Case 4: 352 -> 2*3*5 = 30 and 2+3+5 = 10 and also give only one answer 352 < 550. Case 5: 523 -> 2*3*5 = 30 and 2+3+5 = 10 and also give only one answer 523 < 550. Case 6: 532 -> 2*3*5 = 30 and 2+3+5 = 10 and also give only one answer 532 < 550.

GGRRRRRRR.....Made the same mistake...Forgot to include 1 and chose the answer as A. I should not make similar mistakes in the real exam. Thanks BUnnel.
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Re: Is the three-digit number n less than 550 ? [#permalink]

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31 Oct 2014, 20:06

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