If P and Q represent the hundreds and tens digits, respectively, in th

Question

If P and Q represent the hundreds and tens digits, respectively, in the four-digit number x=8PQ2, is x divisible by 8?

(1) P=4
(2) Q=0

Bunuel · Accepted Answer

If P and Q represent the hundreds and tens digits, respectively, in the four-digit number x=8PQ2, is x divisible by 8?

For a number to be divisible by 2 the  last digit  must be divisible by 2 (so the last digit must be even);
For a number to be divisible by 4 the  last two digits  must be divisible by 4 (04, 08, 12, 16, ..., 96);
For a number to be divisible by 8 the  last three digits  must be divisible by 8 (008, 012, 016, ..., );
etc.

(1) P=4. If Q=0, then the answer is NO, because 402 is not divisible by 8, but if Q=3, then the answer is YES, because 432 is divisible by 8. Not sufficient.

(2) Q=0. In this case the last tow digits are 02, so x is not divisible by 4, which means that it's not divisible by 8 either. Sufficient.

Answer: B.

Hope it's clear.

MarmikUpadhyay · Answer

Given: P and Q represent the hundreds and tens digits, respectively, in the four-digit number x=8PQ2.
Is x divisible by 8?

x is divisible by 8 only if last three digits are divisible by 8.
=> if PQ2 is divisible by 8, then x will be divisible by 8.

Statement 1:
P = 4
PQ2 is divisible by 8 for Q = {3, 7} and for other values of Q, it is not divisible.
Statement 1 is Not Sufficient.

Statement 2:
Q = 0
PQ2 is not divisible by 8 for any value of P, and so x is also not divisible by 8.
Statement 2 is Sufficient.

So, correct answer is option  B .

unraveled · Answer

If P and Q represent the hundreds and tens digits, respectively, in the four-digit number x=8PQ2, is x divisible by 8?
We can take cues from each of the statements. x is divisible by 8 if and only if PQ2 is divisible by 8.

(1) P=4
432 is divisible by 8.
402 is not divisible by 8.

INSUFFICIENT.

(2) Q=0
There is factor that when multiplied with 8 results with a 2 at units place and 0 at tens place.
2 at units place is achieved when 8 is multiplied by a factor with 4 at units place.

More importantly the carry(3 when 8 is multiplied by 4) must either be there or added to 7(odd; a4 being the factor multiplied with 8 to result in PQ2) to result in 0 at tens place in 8PQ2.
However, when any digit is multiplied with 8 it results in an even number. 7 is never possible.

Hence if Q is 0 then PQ2 would never be divisible by 8.

Answer B.

TarunKumar1234 · Answer

If P and Q represent the hundreds and tens digits, respectively, in the four-digit number x=8PQ2, is x divisible by 8?

Stat1: P=4
x = 84Q2, now, if Q= 0 or 1, then x is not divisible by 8. But, if Q = 3 or 7, then then x is divisible by 8. Not sufficient

Stat2: Q=0
x = 8P02, now whatever value of P will be, we never left with 32 or 72 in last. So, it won't be divisible. Sufficient

So, I think B.

donu · Answer

I'm not writing a solution just a tip. This is a classic "C-trap" question.

Right from the jump you know that (1) + (2) is sufficient to tell you whether 8PQ2 is div by 8. But they are trying to trick you into selecting C. Most times when it's so clear that (1) + (2) are sufficient either (1) alone or (2) alone will be sufficient.

When solving these questions, be skeptical of option C. Try to show that (1) or (2) alone is sufficient!

Hope this helps

If P and Q represent the hundreds and tens digits, respectively, in th

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