If A and B are integers, is N an even integer?

Question

(1) 11A + 4B = N 
(2) 5A – 4B = 2N

genericUser · Answer

If A and B are integers, is N an even integer?

(1) 11A + 4B = N
(2) 5A – 4B = 2N

Put B=0 to make life simple

(1)
Plug in numebers
A=1, ko
A=2, ok
Insufficient.

(2)
(5/2)A = N
A=4 ok
A=1 ko
Insufficient.

(1)+(2)
sum two equation
16A=3N
(16/3)A=N
A=3 ok
A=1 ko
Insufficient.

E

Archit3110 · Answer

target is N an even integer given A & B are integers
#1
11A + 4B = N
we can have N as odd when A is odd and N as even when A is even
insufficient
#2
5A-4B=2N
since LHS is 2N i.e. even so value of A has to be even only
but N can be 3 when A = 2 , B = 1 and N = 3 when A = 4 and B = 1
insufficient
from 1 &2 
we can say that A & B are even so value of N is even
option C

ThatDudeKnows · Answer

Evaluate statement (1) alone:
We are multiplying B by an even number, so 4B must be even regardless of whether B is even or odd. If A is odd, 11A will be odd. If A is even, 11A will be even. Do we have enough information to know whether N is even? No. BCE.

Evaluate statement (2) alone:
Similar logic to statement (1), but with a the added element that N could even end up being a fraction, so not only are we not sure whether N is an even integer, we aren't sure it's an integer. Do we have enough information to know whether N is even? No. CE.

Evaluate both statements together:
If we subtract statement (2) from statement (1), we get 6A+8B=-N which is -6A-8B=N. So, N is the sum of -6A (which must be even) and -8B (which must be even). Even plus even must be even. N must be even. Do we have enough information to know whether N is even? Yes. C.

Answer choice C.

BrentGMATPrepNow · Answer

Given : A and B are integers

Target question :    Is N an even integer?

Statement 1 : 11A + 4B = N  
There are several values of A and B that satisfy statement 1. Here are two: 
 Case a : A = 0 and B = 0. In this case, 11A + 4B = 11(0) + 4(0) = 0 = N, which means the answer to the target question is  YES, N is even. 
 Case b : A = 1 and B = 0. In this case, 11A + 4B = 11(1) + 4(0) = 15 = N, which means the answer to the target question is  NO, N is not even. 
Since we can’t answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : 5A – 4B = 2N 
There are several values of A and B that satisfy statement 2. Here are two: 
 Case a : A = 0 and B = 0. In this case, 5A – 4B = 5(0) - 4(0) = 0 = 2N, which means N = 0, which means the answer to the target question is  YES, N is even. 
 Case b : A = 1 and B = 0. In this case, 5A – 4B = 5(1) - 4(0) = 5 = 2N, which means N = 2.5, which means the answer to the target question is  NO, N is not even. 
Since we can’t answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined    
Statement 1 tells us that 11A + 4B = N
Statement 2 tells us that 5A – 4B = 2N
If we subtract the first equation from the second equation we get:  (5A – 4B) - (11A + 4B) = 2N - N 
Simplify:  -6A - 8B = N 
Factor the left side as follows:   2 (-3A - 4B) = N 
Since A and B are integers, we know that (-3A - 4B) must be an integer, which means N is clearly a multiple of   2  , which means   N is even  
Since we can answer the  target question  with certainty, the combined statements are SUFFICIENT

Answer: C

IanStewart · Answer

Each statement is clearly insufficient alone. Using both, from Statement 1 we know N is an integer (because A and B are integers, so 11A + 4B is an integer), and if we add the two equations, we learn 16A = 3N. Since 16A is an even integer, 3N is an even integer, and since N is an integer, N is even (and actually must be a multiple of 16) so the answer is C.

gmatophobia · Answer

Hi IanStewart , BrentGMATPrepNow I solved the question using your approach however, I guess I am missing something

Individual statements are not sufficient, however when we combine the statements we get (inline with your approach)- 16A = 3N From the premise, we know that A is an integer , we don't know if N is an integer . Case 1: Say A = 2 & N = 32/3 16 A = 3N Is N an even Integer = No Case 2: Say A = 6 & N = 2*16 Is N an even integer = Yes Are we not getting both Yes and No, and the answer should be E. What am I missing in here ? P.S - My apologies if the question seem stupid.

BrentGMATPrepNow · Answer

If A is an integer, then 11A is an integer. 
If B is an integer, then 4B is an integer. 
Since 11A + 4B = N, we can be certain that N is an integer.

So any non-integer values of N do not adhere to the given conditions. 
For the examples you provided, try calculating the corresponding value(s) of B, and you'll see the problem.

gmatophobia · Answer

Thank you for the reply ! I understood where did I go wrong.

Posted from my mobile device

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If A and B are integers, is N an even integer?

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If A and B are integers, is N an even integer?

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