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

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Bunuel
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If P and Q represent the hundreds and tens digits, respectively, in th [#permalink] If P and Q represent the hundreds and tens digits, respectively, in th   15 Mar 2021, 00:15
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A
B
C
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E

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55% (hard)

Question Stats:

57% (01:45) correct 43% (01:08) wrong based on 123 sessions
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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

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Bunuel
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Re: If P and Q represent the hundreds and tens digits, respectively, in th [#permalink] If P and Q represent the hundreds and tens digits, respectively, in th   16 Mar 2021, 01:15
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Bunuel wrote:
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

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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.
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Re: If P and Q represent the hundreds and tens digits, respectively, in th [#permalink] If P and Q represent the hundreds and tens digits, respectively, in th   15 Mar 2021, 01:01
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Bunuel wrote:
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


Divisibility by 8 or \(2^3\) depends on the last 3 digits, PQ2.

(1) P=4
Nothing about Q.
If Q=0, then No.
If Q=3, then yes.

(2) Q=0
SO the last two digits are 02.
Property of 'Divisibility' by 4 or \(2^2\) depends on the last 2 digits, Q2 or 02.
Now the number is never divisible by 4, so it will never be divisible by 8 also.
8P02=8P00+2=8P*100+2
8P*100 is divisible by 4, thus 2 is the remainder.
Sufficient as answer is NO.

B
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Re: If P and Q represent the hundreds and tens digits, respectively, in th [#permalink] If P and Q represent the hundreds and tens digits, respectively, in th   15 Mar 2021, 10:39
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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
then, x =84Q2, it can be divisible by 8 or not. Not sufficient.

Stat2: Q=0
then, x =8P02, we can have any digit for P, but x won't be divisible by 8.

x =8P02, if last two digits is 02, x won't be divisible by 8.
x =8P02, if last two digits is 22, x won't be divisible by 8.
x =8P02, if last two digits is 42, x won't be divisible by 8.
x =8P02, if last two digits is 62, x won't be divisible by 8.
x =8P02, if last two digits is 82, x won't be divisible by 8.
Sufficient.

So, I think B. :)
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Re: If P and Q represent the hundreds and tens digits, respectively, in th [#permalink] If P and Q represent the hundreds and tens digits, respectively, in th   16 Mar 2021, 00:09
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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

x = 84Q2
For Q=2, 8422 is not divisible
For Q=3, 8432 is divisible
Not sufficient

(2) Q=0

x = 8P02
The last two digits are not divisible by 4. So, 8P02 is not divisible by 8.
Sufficient

Option B

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If P and Q represent the hundreds and tens digits, respectively, in th [#permalink] If P and Q represent the hundreds and tens digits, respectively, in th   Updated on: 15 Mar 2021, 01:48
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Is 8PQ2 divisible by 8?
Divisibility rule of 8:
If the last three digits of a number are divisible by 8, then the number is completely divisible by 8.
Last 3 digits in 8PQ2 are PQ2.
We will check last three digits only.

Statement 1:
P = 4
=>PQ2 = 4Q2.
If Q = {3, 7}, then PQ2 is divisible by 8.
For all other values of Q, PQ2 is not divisible by 8
Statement 1 is Not Sufficient.

Statement 2:
Q = 0
=>PQ2 = P02
For any value of P, PQ2 is not divisible by 8
Statement 2 is Sufficient.

So, correct answer is option B.

Originally posted by MarmikUpadhyay on 15 Mar 2021, 01:08.
Last edited by MarmikUpadhyay on 15 Mar 2021, 01:48, edited 2 times in total.
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Re: If P and Q represent the hundreds and tens digits, respectively, in th [#permalink] If P and Q represent the hundreds and tens digits, respectively, in th   15 Mar 2021, 01:33
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MarmikUpadhyay wrote:
Is 8PQ2 divisible by 8?
Divisibility rule of 8:
If the last three digits of a number are divisible by 8, then the number is completely divisible by 8.
Last 3 digits in 8PQ2 are PQ2.
We will check last three digits only.

Statement 1:
P = 4
=>PQ2 = 4Q2.
If Q = {3, 7}, then PQ2 is divisible by 8.
For all other values of Q, PQ2 is not divisible by 8
Statement 1 is Not Sufficient.

Statement 2:
Q = 0
=>PQ2 = P02
If P = {1, 3, 5, 7, 9}, then PQ2 is divisible by 8.
For even values of P, PQ2 is not divisible by 8
Statement 2 is also Not Sufficient.

Statement 1 and Statement 2 combined:
P = 4 and Q = 0
=> PQ2 = 402
402 is not divisible by 8. Therefore, 8402 is also not divisible by 8.
Statement 1 and Statement 2 together are Sufficient.

So, correct answer is option C.



You will have to look into your solution.

102, 202, 302 and so on are not divisible by 4, leave aside 8.
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