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e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3078
B is a two-digit number, which can be expressed as the product of a an  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 41% (02:31) correct 59% (02:29) wrong based on 176 sessions

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Common Mistakes One Must Avoid in Remainders – Practice question 3

B is a two-digit number, which can be expressed as the product of a and e, where both a and e are positive integers. What is the remainder when B is divided by 12?

(1) a is an even number greater than 5.
(2) a, b, c, d, and e are 5 consecutive integers, in increasing order.

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are NOT sufficient.

To read the article: Common Mistakes One Must Avoid in Remainders

_________________

Originally posted by EgmatQuantExpert on 24 Oct 2018, 07:05.
Last edited by EgmatQuantExpert on 21 Nov 2018, 03:57, edited 4 times in total.
Math Expert V
Joined: 02 Aug 2009
Posts: 8004
Re: B is a two-digit number, which can be expressed as the product of a an  [#permalink]

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B is a two-digit number, which can be expressed as the product of a and e, where both a and e are positive integers. What is the remainder when B is divided by 12?

(1) a is an even number greater than 5.
Insufficient

(2) a, b, c, d, and e are 5 consecutive integers, in increasing order.
So e =a+4...
If a is 2, e is 6, so ae=12...remainder is 0
If a=3, e is 7 so ae =21..remainder is 9
Insufficient

Combined..
Min value of e is 6, so e is 10, ae is 60.. remainder is 0
The next value of a is 8 and e will become 12, ae is 96..remainder again is 0
Next value of a as 10 is not possible as ae will become 10*14=140, a 3-digut number
So remainder is always 0
Sufficient

C
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e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3078
Re: B is a two-digit number, which can be expressed as the product of a an  [#permalink]

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2

Solution

Given:
• B is a two-digit number.
• B = a x e, where both a and e are positive integers.

To find:
• The remainder, when B is divided by 12.

Analysing Statement 1
As per the information given in statement 1, a is an even number greater than 5.
• From this statement, we cannot determine what is e.
• Therefore, we can’t also determine the value of B.

Hence, statement 1 is not sufficient to answer the question.

Analysing Statement 2
As per the information given in statement 2, a, b, c, d, and e are consecutive integers, in increasing order.

Now there can be multiple possibilities:

For example,
• If a = 1, then e = 5, and B = 1 x 5 = 5, which is not divisible by 12.
• However, if a = 2, then e = 6, and B = 2 x 6 = 12, which is divisible by 12.

As we get different remainders of different values of B, we can’t determine the answer from this statement.

Combining Both Statements
We know that a, b, c, d, and e are consecutive positive integers, in increasing order, where a is an even number greater than 5.

Hence, out of the five numbers, a, c, and e are even, and b and d are odd.
• Now, if a = 6, then e = 10, and B = 6 x 10 = 60, which is divisible by 12.
• If a = 8, then e = 12, and B = 8 x 12 = 96, which is divisible by 12.

We can’t have a = 10 or greater than 10, as if a = 10, then e = 14 and B will not remain a 2-digit number.

Therefore, only two possibilities exist, and in both cases, the remainder is 0 when B is divided by 12.

Hence, the correct answer is option C.

_________________ Re: B is a two-digit number, which can be expressed as the product of a an   [#permalink] 30 Oct 2018, 06:23
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