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# If 4s - 3t = 10 where s and t are integers, which of the following can

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Manager
Joined: 17 Mar 2015
Posts: 86
If 4s - 3t = 10 where s and t are integers, which of the following can  [#permalink]

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04 Feb 2018, 12:23
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Difficulty:

55% (hard)

Question Stats:

60% (02:16) correct 40% (02:16) wrong based on 71 sessions

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If 4s - 3t = 10 where s and t are integers, which of the following cannot be true?

a. s and t have same signs.
b. s and t have opposite signs.
c. there is a solution such that t is divisible by 8.
d. there is solution such that when s is divided by 3, remainder is 1.
e .there is a solution such that both s and t are positive integers.
Director
Joined: 31 Jul 2017
Posts: 517
Location: Malaysia
Schools: INSEAD Jan '19
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
Re: If 4s - 3t = 10 where s and t are integers, which of the following can  [#permalink]

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04 Feb 2018, 13:10
prince00113 wrote:
If 4s - 3t = 10 where s and t are integers, which of the following cannot be true?

a. s and t have same signs.
b. s and t have opposite signs.
c. there is a solution such that t is divisible by 8.
d. there is solution such that when s is divided by 3, remainder is 1.
e .there is a solution such that both s and t are positive integers.

4s - 3t = 10. ---> 4s = 10 + 3t

a. $$t = 2, s = 4$$
b. $$t = -2, s= 1$$
c. $$t = \frac{10}{4} + 6k$$ --- No Such Solution
d. $$t = 2, s = 4$$
e. $$t= 2, s = 4.$$
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Joined: 07 Dec 2014
Posts: 1151
If 4s - 3t = 10 where s and t are integers, which of the following can  [#permalink]

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04 Feb 2018, 14:15
prince00113 wrote:
If 4s - 3t = 10 where s and t are integers, which of the following cannot be true?

a. s and t have same signs.
b. s and t have opposite signs.
c. there is a solution such that t is divisible by 8.
d. there is solution such that when s is divided by 3, remainder is 1.
e .there is a solution such that both s and t are positive integers.

a. is true for s=4;t=2
b. is true for s=1;t=-2
c. is not true:
4s-3t=10
→t=(4s-10)/3
→t/8=(4s-10)/24
4s-10 is not a multiple of 4
t≠integer
c
If 4s - 3t = 10 where s and t are integers, which of the following can &nbs [#permalink] 04 Feb 2018, 14:15
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# If 4s - 3t = 10 where s and t are integers, which of the following can

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