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Two natural numbers a and b are such that a = 3b + b^2

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Two natural numbers a and b are such that a = 3b + b^2  [#permalink]

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New post 06 Jan 2019, 08:21
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A
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C
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E

Difficulty:

  55% (hard)

Question Stats:

55% (01:07) correct 45% (01:16) wrong based on 38 sessions

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Two natural numbers a and b are such that a = 3b + b^2. Is 'a' a multiple of 5?

(1) b is a multiple of 2

(2) b is a factor of 10
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Re: Two natural numbers a and b are such that a = 3b + b^2  [#permalink]

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New post 07 Jan 2019, 21:38
From statement 1:

b is a multiple of 2.
b can be 0, 2, 4, 6, etc.
If b is 0 and 2, then a will be a multiple of 5.
If b is 4, then a will not be a multiple of 5.
Hence statement 1 is insufficient.

From statement 2:

b is a factor of 10.
b is 1, 2, 5, 10.
If b is 2, 5 or 10. Then a will be a multiple of 5.
If b is 1, then a will not be a multiple of 5.
Insufficient.

Combining both gives the value of b as 2 or 10.
For 2 or 10, a will be a multiple of 5.
Hence sufficient.

C is the answer.
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Re: Two natural numbers a and b are such that a = 3b + b^2  [#permalink]

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New post 07 Jan 2019, 23:46
Hi,


Given, “a” and “b” are natural numbers.

That is, “a” and “b” are positive integers.

Such that, a = 3b + b^2.

Question:

Is “a” multiple of 5 ?

i.e., whether a = 5, 10, 15…..?

Statement I is insufficient:

b is a multiple of 2.

“b” is a positive integer and multiple of 2..

So, “b” can be 2,4,6,8,10…

If b = 2, then

a = 3b + b^2 = 6 +4 = 10 and is a multiple of 5. Answer to the question is YES.

But if b = 4, then

a = 3b + b^2 = 12 + 16 = 28 and it is not a multiple of 5. Answer to the question is NO.

Statement II is insufficient:

b is a factor of 10

So, “b” values are 1, 2, 5 or 10.

If b = 2, then

a = 3b + b^2 = 6 +4 = 10 and is a multiple of 5. Answer to the question is YES.

But if b = 1, then

a = 3b + b^2 = 3 + 1 = 4 and it is not a multiple of 5. Answer to the question is NO.

Together it is sufficient.

Values of “b” which satisfy both statement I and II is 2 and 10.

So,

If b = 2, then

a = 3b + b^2 = 6 +4 = 10 and is a multiple of 5. Answer to the question is YES.

And if b = 10, then

a = 3b + b^2 = 30 + 100 = 130 and it is also a multiple of 5. Answer to the question is again YES.

So together it is sufficient.

Answer is C.

Hope this helps.
Regards,
Junaid.
Byjus GMAT Quant Expert
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Re: Two natural numbers a and b are such that a = 3b + b^2 &nbs [#permalink] 07 Jan 2019, 23:46
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Two natural numbers a and b are such that a = 3b + b^2

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