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31 May 2022, 08:28
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Difficulty:
95%
(hard)
Question Stats:
23% (01:41) correct
77%
(01:45)
wrong
based on 141
sessions
History
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Not Attempted Yet
If A and B are integers, is B even?
(1) 14A – 11B = 7N
(2) 14A – 11B = 2N
(1) 14A – 11B = 7N
(2) 14A – 11B = 2N
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31 May 2022, 12:40
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Step 1: Analyse Question Stem
A and B are integers.
We have to find if B is even.
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1: 14A – 11B = 7N
There is no information about N; it could be a fraction or an integer.
The best strategy is to reorganise the equation to have B on one side and then test cases.
Reorganising, 11B = 14 A – 7 N.
If B = 1, A = 1 and N = \(\frac{3}{7}\), the equation is satisfied. In this case, B is not even.
If B = 2, A = 2 and N = \(\frac{6}{7}\), the equation is satisfied. In this case, B is even.
The data in statement 1 is insufficient to answer the question with a definite YES or NO.
Statement 1 alone is insufficient. Answer options A and D can be eliminated.
Statement 2: 14A – 11B = 2N
Again, there is no information about N. We can follow a similar strategy of reorganising the equation and testing cases.
Reorganising, 11B = 14 A – 2N
If B = 1, A = 1 and N = \(\frac{3}{2}\), the equation is satisfied. In this case, B is not even.
If B = 2, A = 2 and N = 3, the equation is satisfied. In this case, B is even.
The data in statement 2 is insufficient to answer the question with a definite YES or NO.
Statement 2 alone is insufficient. Answer option B can be eliminated.
Step 3: Analyse Statements by combining
From statement 1: 14A – 11B = 7N
From statement 2: 14A – 11B = 2N
Therefore, 7N = 2N. This is possible only if N = 0.
Therefore, 14 A – 11 B = 0; or 14 A = 11 B.
Hence, \(\frac{A }{ B}\) = \(\frac{11 }{ 14}\).
Since B is an integer, it can be concluded that B is a multiple of 14. Any multiple of 14 is always even.
Therefore, B is even.
The combination of statements is sufficient to answer the question with a definite YES.
Statements 1 and 2 together are sufficient. Answer option E can be eliminated.
The correct answer option is C.
A and B are integers.
We have to find if B is even.
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1: 14A – 11B = 7N
There is no information about N; it could be a fraction or an integer.
The best strategy is to reorganise the equation to have B on one side and then test cases.
Reorganising, 11B = 14 A – 7 N.
If B = 1, A = 1 and N = \(\frac{3}{7}\), the equation is satisfied. In this case, B is not even.
If B = 2, A = 2 and N = \(\frac{6}{7}\), the equation is satisfied. In this case, B is even.
The data in statement 1 is insufficient to answer the question with a definite YES or NO.
Statement 1 alone is insufficient. Answer options A and D can be eliminated.
Statement 2: 14A – 11B = 2N
Again, there is no information about N. We can follow a similar strategy of reorganising the equation and testing cases.
Reorganising, 11B = 14 A – 2N
If B = 1, A = 1 and N = \(\frac{3}{2}\), the equation is satisfied. In this case, B is not even.
If B = 2, A = 2 and N = 3, the equation is satisfied. In this case, B is even.
The data in statement 2 is insufficient to answer the question with a definite YES or NO.
Statement 2 alone is insufficient. Answer option B can be eliminated.
Step 3: Analyse Statements by combining
From statement 1: 14A – 11B = 7N
From statement 2: 14A – 11B = 2N
Therefore, 7N = 2N. This is possible only if N = 0.
Therefore, 14 A – 11 B = 0; or 14 A = 11 B.
Hence, \(\frac{A }{ B}\) = \(\frac{11 }{ 14}\).
Since B is an integer, it can be concluded that B is a multiple of 14. Any multiple of 14 is always even.
Therefore, B is even.
The combination of statements is sufficient to answer the question with a definite YES.
Statements 1 and 2 together are sufficient. Answer option E can be eliminated.
The correct answer option is C.
General Discussion
Archit3110
Major Poster
Updated on: 31 May 2022, 12:44
Originally posted by Archit3110 on 31 May 2022, 11:39.
Last edited by Archit3110 on 31 May 2022, 12:44, edited 1 time in total.
Last edited by Archit3110 on 31 May 2022, 12:44, edited 1 time in total.
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If A and B are integers, is B even?
(1) 14A – 11B = 7N
(2) 14A – 11B = 2N
#1
Since A& B are integers so
A&B have to be factors of 7
Case 1
14*7-11*7 =7*3
B is odd
Case 2
14*14-11*14= 7*6
B Is even insufficient
#2
14A-11B =2N
Irrespective of A being odd or even 14A shall always be even so B has to be even as well
Also case when A=B=1 AND N 3/2 Insufficient
From 1&2
At N =0 we get A/B=11/14
sufficient
Posted from my mobile device
(1) 14A – 11B = 7N
(2) 14A – 11B = 2N
#1
Since A& B are integers so
A&B have to be factors of 7
Case 1
14*7-11*7 =7*3
B is odd
Case 2
14*14-11*14= 7*6
B Is even insufficient
#2
14A-11B =2N
Irrespective of A being odd or even 14A shall always be even so B has to be even as well
Also case when A=B=1 AND N 3/2 Insufficient
From 1&2
At N =0 we get A/B=11/14
sufficient
Posted from my mobile device
