for sure the answer is B, but to me this problem is too time consuming,
it will be great if somebody shares any shortcut
17a+19b=?, find b-?
(1) a+b=8 not suff
(2) 17a+19b=140, we must prove the only integers for a and b exist
here b=2,a=6 (17*6+19*2=140)
and there are no others integers for a and b that give proper result
Cakes
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Source: Beat The GMAT — Data Sufficiency |
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ldoolitt
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If you wanted to SOLVE the problem (ie a PS problem) first I would subtract 19b from both sides, then divide by 17clock60 wrote:for sure the answer is B, but to me this problem is too time consuming,
it will be great if somebody shares any shortcut
17a+19b=?, find b-?
(1) a+b=8 not suff
(2) 17a+19b=140, we must prove the only integers for a and b exist
here b=2,a=6 (17*6+19*2=140)
and there are no others integers for a and b that give proper result
(17b/17) = (140/17) - (19a/17)
You know that the left side is an integer so the right side must also be an integer
integer = (136/17) + (4/17) - (17/17) * a - (2/17) * a
integer = integer + 4/17 - integer - (2/17) * a
therefore 4/17 - (2/17) * a must be an integer to remove fractions. a = 2 is the only positive solution that could also satisfy the stem equation (19, etc would work but couldn't possibly satisfy the original equation)
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clock60
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hi Idoolitt
thanks for sharing, but can you elaborate i little bit more
why first I would subtract 19b from both sides, then divide by 17
it sounds great but why in that order
what if substract 17a from both parts and then to divide by 19?
or it does not matter?
thanks for sharing, but can you elaborate i little bit more
why first I would subtract 19b from both sides, then divide by 17
it sounds great but why in that order
what if substract 17a from both parts and then to divide by 19?
or it does not matter?
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ldoolitt
- Master | Next Rank: 500 Posts
- Posts: 184
- Joined: Sat Apr 14, 2007 9:23 am
- Location: Madison, WI
- Thanked: 17 times
Does not matterclock60 wrote:hi Idoolitt
thanks for sharing, but can you elaborate i little bit more
why first I would subtract 19b from both sides, then divide by 17
it sounds great but why in that order
what if substract 17a from both parts and then to divide by 19?
or it does not matter?
(19a/19) = (140/19) - (17b/19)
integer = (133/19) + (7/19) - (19/19) * b + (2/19) * b
integer = integer + 7/19 - integer + (2/19) * b
7/19 + (2/19)*b = integer
b=6 works there
