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04 Jul 2021, 11:35
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
72% (00:56) correct
28%
(01:01)
wrong
based on 61
sessions
History
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Not Attempted Yet
What is the sum of positive integers x and y ?
(1) 3x + 2y = 14 - x
(2) 2x + 3y = 15 - x
(1) 3x + 2y = 14 - x
(2) 2x + 3y = 15 - x
04 Jul 2021, 13:33
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Bunuel
There are two ways we can answer this question:
1. We can somehow determine x,y individually and then solve for x+y ==> Look for trap here
2. We can somehow rearrange the given terms and get x+y directly
(1) often results in a trap because mind immediately goes to "2 equations 2 variables" and hence C, however the fact is that (2) is also possible and you do not need to know x & y individually for that.
There is an additional possible trap here, x & y are given to be positive integers - and that is additional information we need to take into account.
a) Rearrange to 4x+2y = 14. Cannot get clear x+y here without knowing individual values of x,y - or can we? Lets see if that is indeed true
Since x,y are true and LHS is sum of two even terms, lets express 14 in terms of two positive even terms
12, 2 ==> x=3, y=1 => x+y=4
10, 4 ==> Not possible
8, 6 ==> x=2, y=3 => x+y=5
6, 8 ==> We can actually stop since we are already getting two different values of x+y. INSUFF
b) Rearrange to 3x + 3y = 15 => x+y = 5. SUFF
So (B).
06 Jul 2021, 00:11
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Bunuel
1)3x + 2y = 14 - x
3x + x + 2y = 14
4x + 2y = 14
x + 2y = 7
x = 1, y = 3
x = 3, y = 2 - Insufficient!
2)2x + 3y = 15 - x
3x + 3y = 15
x + y = 5 - Sufficient. (B), IMO!
