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17 Jul 2019, 04:52
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C
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Difficulty:
45%
(medium)
Question Stats:
66% (02:02) correct
34%
(01:46)
wrong
based on 248
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If a and b are positive integers, is a divisible by 7?
(1) a + 5b is divisible by 7.
(2) When b is divided by 7, the remainder is 2.
(1) a + 5b is divisible by 7.
(2) When b is divided by 7, the remainder is 2.
21 Jul 2019, 01:35
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Dillesh4096
Is a divisible by 7 ?
(1) a + 5b is divisible by 7.
--> a + 5b = 7k, for any positive integer k
--> a = 7k - 5b
Nothing can be said about the divisibility of a by 7
Insufficient
(2) When b is divided by 7, the remainder is 2
--> b = 7m + 2, for any non-negative integer m
Does not talk about the value 'a'
Insufficient
Combining (1) & (2),
a = 7k - 5b
--> a = 7k - 5(7m + 2)
--> a = 7k - 35m - 10
--> a = 7(k - 5m) - 10
or
--> a = 7(k - 5m) - 14 + 4
--> a = 7(k - 5m - 2) + 4
So, a is definitely not divisible by 7 (Since, Remainder = 4)
Sufficient
Option C
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General Discussion
18 Jul 2019, 02:05
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An approach that works really well on questions related to divisibility and remainders, is the plugging in approach. When you combine this with a little bit of analysis of the statements based on concepts, the plugging in approach works even better.
From the question data, we know that a and b are positive integers.
From statement I, we know that a + 5b is divisible by 7. This means, we can write an equation like the one below:
a + 5b = 7k, where k is a positive integer again. When we plug in values for k, it will allow us to pick corresponding values for a and b.
If k = 1, a = 2 and b = 1. In this case, a is not divisible by 7. The answer to the main question will be a NO.
If k = 6, a = 7 and b = 7. In this case, a is divisible by 7. The answer to the main question will be a YES.
Hence, statement I alone is insufficient. Answer options A and D can be eliminated. Possible answer options are B, C or E.
From statement II, we know that b can be written as, b = 7x + 2. So, b can be 2 or 9 or 16 and so on depending on the value of x.
However, statement II tells us nothing about the value of a, which is what is needed to answer the question. Therefore, statement II alone is insufficient.
Answer option B can be eliminated.
Combining statements I and II, we have,
b = 2 or 9 or 16 and so on.
We also have a + 5b = 7k. Let us plug in the values of b in this equation, so that we obtain a multiple of 7 (the RHS).
If b = 2, a = 4 so that a+5b is divisible by 7. In this case, a is not divisible by 7.
If b = 9, a = 4 so that a+5b is divisible by 7. In this case also, a is not divisible by 7.
For every value of b you plug in, you will get the value of a as 4. Therefore, statement I and II are sufficient when taken together.
The correct answer option is C.
b = 7x + 2.
So, a + 5b = a + 5 (7x + 2) = a + 35 x + 10 = (35x + 7) + 3 + a.
If a + 5b has to be divisible by 7, 3 + a has to be divisible by 7. a has to be 4.
After solving the question using the plugging in approach, analyzing it using concepts and seeing WHY a has to be 4 will help you build concepts. It will also help you build confidence in yourself because you know that you can back your values through concepts, as and when needed.
Hope this helps!
From the question data, we know that a and b are positive integers.
From statement I, we know that a + 5b is divisible by 7. This means, we can write an equation like the one below:
a + 5b = 7k, where k is a positive integer again. When we plug in values for k, it will allow us to pick corresponding values for a and b.
If k = 1, a = 2 and b = 1. In this case, a is not divisible by 7. The answer to the main question will be a NO.
If k = 6, a = 7 and b = 7. In this case, a is divisible by 7. The answer to the main question will be a YES.
Hence, statement I alone is insufficient. Answer options A and D can be eliminated. Possible answer options are B, C or E.
From statement II, we know that b can be written as, b = 7x + 2. So, b can be 2 or 9 or 16 and so on depending on the value of x.
However, statement II tells us nothing about the value of a, which is what is needed to answer the question. Therefore, statement II alone is insufficient.
Answer option B can be eliminated.
Combining statements I and II, we have,
b = 2 or 9 or 16 and so on.
We also have a + 5b = 7k. Let us plug in the values of b in this equation, so that we obtain a multiple of 7 (the RHS).
If b = 2, a = 4 so that a+5b is divisible by 7. In this case, a is not divisible by 7.
If b = 9, a = 4 so that a+5b is divisible by 7. In this case also, a is not divisible by 7.
For every value of b you plug in, you will get the value of a as 4. Therefore, statement I and II are sufficient when taken together.
The correct answer option is C.
b = 7x + 2.
So, a + 5b = a + 5 (7x + 2) = a + 35 x + 10 = (35x + 7) + 3 + a.
If a + 5b has to be divisible by 7, 3 + a has to be divisible by 7. a has to be 4.
After solving the question using the plugging in approach, analyzing it using concepts and seeing WHY a has to be 4 will help you build concepts. It will also help you build confidence in yourself because you know that you can back your values through concepts, as and when needed.
Hope this helps!
