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product of their digits is 210

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by sanju09 » Tue Jul 27, 2010 12:57 am
How many positive integers less than 10,000 are such that the product of their digits is 210?
A) 24
B) 30
C) 48
D) 54
E) 72

[spoiler]Source: Beat The GMAT Challenge Question - July 26, 2010[/spoiler]
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by 4GMAT_Mumbai » Tue Jul 27, 2010 1:13 am
Hi,

210 = 2*3*7*5

Number of 3 digit numbers = 675, 657, 756, 765, 567, 576. This is possible because 2 times 3 equals 6. There is no other pair within 2, 3, 7, 5 whose product yields a one digit number.

Number of 4 digit numbers involving 1, 6, 5, 7 = 4! = 24

Number of 4 digit numbers involving 2, 3, 5, 7 = 4 * 3 * 2 * 1 = 24

Overall, answer = 54.

The obvious trap is for somebody to fall for 24 (no wonder, it is choice A).

Is this right ... Thanks.
Last edited by 4GMAT_Mumbai on Tue Jul 27, 2010 1:29 am, edited 1 time in total.
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by sanju09 » Tue Jul 27, 2010 1:21 am
4GMAT_Mumbai wrote:Hi,

210 = 2*3*7*5

Number of 3 digit numbers = 675, 657, 756, 765, 567, 576. This is possible because 2 times 3 equals 6. There is no other pair within 2, 3, 7, 5 whose product yields a one digit number.

Number of 4 digit numbers = 4 * 3 * 2 * 1 = 24

Overall, answer = 30.

The obvious trap is for somebody to fall for 24 (no wonder, it is choice A).

Is this right ... Thanks.
I don't know since I haven't given it a try as yet, but choice [spoiler]D[/spoiler] has received most of the votes at the site where it was originally flashed.
The mind is everything. What you think you become. -Lord Buddha



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by 4GMAT_Mumbai » Tue Jul 27, 2010 1:31 am
sanju09 wrote: I don't know since I haven't given it a try as yet, but choice [spoiler]D[/spoiler] has received most of the votes at the site where it was originally flashed.
Thanks Sanju ... I edited the old post. I had missed the four digit numbers involving 1, 6, 5, 7.
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by saurabhmahajan » Tue Jul 27, 2010 2:38 am
adding 24 plus the 6 three digit nos add up to 30...
then how can be the answer 54.
please explain.
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by selango » Tue Jul 27, 2010 2:50 am
saurabhmahajan wrote:adding 24 plus the 6 three digit nos add up to 30...
then how can be the answer 54.
please explain.
Number of 3 digit numbers = 675, 657, 756, 765, 567, 576 =6

Number of 4 digit numbers involving 1, 6, 5, 7 = 4! = 24

Number of 4 digit numbers involving 2, 3, 5, 7 = 4! = 24

Total=6+24+24=54
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by sanju09 » Tue Jul 27, 2010 2:52 am
saurabhmahajan wrote:adding 24 plus the 6 three digit nos add up to 30...
then how can be the answer 54.
please explain.
4 digit numbers are also accommodated within 10000, that's why.
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