Is the three-digit number

[Bhaskar]

Is the three-digit number less than 550?

(1) The product of the digits in n is 30
(2) The sum of the digits in n is 10

I think the answer should be A, but GMATprep says that the answer should be C. Why?

My reasoning:
(1) 2x5x3=30
532<550 so yes we can answer the three digit number is less than 550.

(2) not sufficient because 2+4+4=10 and 442<550 but 7+2+1=10 and 721>550

I don't understand why it is C.

[guest]

You are forgetting 1,6,5 combination...even i forgot it and then someone explained it to me. :) With 1,6,5 and 2,3,5 we can't answer with A and hence would need both as second one eliminates1,6,5 combination

[RonPurewal]

You are forgetting 1,6,5 combination...even i forgot it and then someone explained it to me. :) With 1,6,5 and 2,3,5 we can't answer with A and hence would need both as second one eliminates1,6,5 combination

you got it.

don't forget 1 as a possible component of a product! if you're thinking solely in terms of primes, then it's easy to forget about 1 (because 1 isn't prime).

if you ever get a problem like this again, though, you'll be sure not to forget 1, though, because you'll be reminded of this problem. that's the power of making mistakes - you'll learn the relevant lessons much better than you would if you hadn't made the mistakes.

[rkafc81]

i tried to solve it by generating test cases and proving insufficiency for each statement...

(1)

2x5x3
5x3x2
6x5x1 xyz = 651
5x6x1
3x5x2 xyz = 352

NOT SUFF.

(2)

2+5+3
3+5+2
5+5+0 xyz = 550
4+4+2
5+4+1
6+3+1 xyz = 631

NOT SUFF.

1+2

??

i got stuck here trying to put the info from both statements together and I don't know why...

I think when I did it, i wasn't confident that i'd generated enough numbers and so i couldnt see how to put the info from both statements together...

or for these types of questions, do I just use the conditions from both statements to eliminate test cases that don't meet both conditions, and then see if the remaining test cases are sufficient?

thanks!

[RonPurewal]

hi,

i tried to solve it by generating test cases and proving insufficiency for each statement...

that's a good strategy. it's highly effective on a great many data sufficiency problems, including this one.

(1)

2x5x3
5x3x2
6x5x1 xyz = 651
5x6x1
3x5x2 xyz = 352

NOT SUFF.

this works, although i'm a little confused. why did you ignore the first two cases?
i.e., your very first case (253) gives a "yes" answer, but you don't seem to have recognized that (because you kept going until you got 352).
so, you could have stopped as soon as you reached 651.

(2)

2+5+3
3+5+2
5+5+0 xyz = 550
4+4+2
5+4+1
6+3+1 xyz = 631

NOT SUFF.

same here -- you're done as soon as you find 253 and 550.

also, make sure you read the question more carefully/literally. the two cases you actually wrote out here -- 550 and 631 -- are both "no" to the question.

1+2

??

i got stuck here trying to put the info from both statements together and I don't know why...

I think when I did it, i wasn't confident that i'd generated enough numbers and so i couldnt see how to put the info from both statements together...

this is where you have to start getting systematic. i don't see any obvious shortcut to combining the statements -- but the good news is that you don't need a shortcut, because there aren't very many cases to consider.
on any DS problem with only a modest number of cases, don't be afraid to just WRITE OUT ALL THE CASES.

for the first statement, the only viable combinations of digits are 2,3,5 and 1,5,6. i think you basically figured this out above; if you didn't, you'd figure it out soon enough after trying (unsuccessfully) to find other groups of digits.
this is all possible cases:
* all possible orderings of 2,3,5
* all possible orderings of 1,5,6
the former will satisfy statement 2 as well; the second won't. so, the numbers that satisfy both statements together are the different orderings of 2,3,5.

from those numbers, can you get a "yes" to this question? sure you can -- just make any random number out of these digits and you'll get a "yes".
can you get a "no" to the question? nope -- the biggest number you can make with these digits is 532.
so, definite "yes". sufficient.

or for these types of questions, do I just use the conditions from both statements to eliminate test cases that don't meet both conditions, and then see if the remaining test cases are sufficient?

that's a very potent approach, especially if there are only a modest number of cases to begin with.

[rkafc81]

great thanks Ron

yeah I guess I generated heaps of cases before actually thinking about them - where i could have actually made my life easier by finding one 'yes' case and one 'no' case ... will do that next time!

[tim]

:)