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 1As 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 2As 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 StatementsWe 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.
Answer: CIt was confusing to solve for B in the question and have something about b in statement 2. Thankfully it was given that B is a 2-digit number. Can something of this sort happen in the actual exam?