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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 06 May 2010, 11:31
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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 digits in n is 10.
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Re: GMAT PREP (DS) [#permalink] New post 06 May 2010, 13:19
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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 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: GMAT PREP (DS) [#permalink] New post 06 May 2010, 22:07
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 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.
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Re: GMAT PREP (DS) [#permalink] New post 07 May 2010, 03:49
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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Re: Gmat Prep problem [#permalink] New post 17 Sep 2010, 11:06
Should be C.

Here is how I got there:

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, 11:17, edited 1 time in total.
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Re: Gmat Prep problem [#permalink] New post 17 Sep 2010, 11:14
rgtiwari wrote:
Please explain the answer..


Statement 1 alone
Case 1: 651 -> 6*5*1 = 30 => 651 < 550 - false
Case 2: 235 -> 2*3*5 = 30 => 235< 550 - true

Not Sufficient.

Statement 2 alone
Case 1: 235 -> 2+3+5 = 10 => 235 < 550 - true
Case 2: 550 -> 5+5+0 = 10 => 550 < 550 - false

Not Sufficient

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.

Hence C
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Re: GMAT PREP (DS) [#permalink] New post 18 Sep 2010, 17:06
ha....I also forgot "1" as a factor....thanks for reminding.....
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Re: GMAT PREP (DS) [#permalink] New post 19 Sep 2010, 17:24
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: GMAT PREP (DS) [#permalink] New post 21 Jan 2013, 23:54
n = xyz, is xyz < 550?

1. digits product is 30
Let n = 651, NO!
Let n = 516, YES!
INSUFFICIENT.

2. digits sum is 10
Let n = 550, NO!
Let n = 505, YES!
INSUFFICIENT

Digits that produce a product of 30:
{6,5,1}
{2,3,5}

But, the sum must be 10 and only {2,3,5} produce a sum of 10.
And the largest number is 532 which is less than 550

Answer: C
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Re: GMAT PREP (DS)   [#permalink] 21 Jan 2013, 23:54
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