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Number system sum

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by kvcpk » Sun Jul 04, 2010 5:49 am
winnerhere wrote:Each of the letters P,Q,R and S represent a non equal digit.

Q > P and PR x QR = SSS . Then (PR)^2 =

a)676

b)441

c)625

d)729
Hi,

sss is a 3 digit number.. SO it can be 111 or 222 or 333 .... 999
111 = 37 *03. 2 3's are present. SO ruled out
222 = 37 * 06 or 74 * 03
333 = 37 * 09
444 = 37 * 12
555 = 37 * 15
666 = 37 * 18
777 = 37 * 21
888 = 37 * 24
999 = 37 * 27 Ruled out

Look at the options now:
a)676 = 26^2 - not on our list

b)441 = 21^2 on our list

c)625 =25^2 noton our list

d)729 = on our list but ruled out beacuse of same digits

Hence B

Hope this helps!!
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by winnerhere » Sun Jul 04, 2010 5:58 am
Thanks kvcpk :)

That helped :)
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by mj78ind » Sun Jul 04, 2010 8:27 am
kvcpk wrote:
winnerhere wrote:Each of the letters P,Q,R and S represent a non equal digit.

Q > P and PR x QR = SSS . Then (PR)^2 =

a)676

b)441

c)625

d)729
Hi,

sss is a 3 digit number.. SO it can be 111 or 222 or 333 .... 999
111 = 37 *03. 2 3's are present. SO ruled out
222 = 37 * 06 or 74 * 03
333 = 37 * 09
444 = 37 * 12
555 = 37 * 15
666 = 37 * 18
777 = 37 * 21
888 = 37 * 24
999 = 37 * 27 Ruled out

Look at the options now:
a)676 = 26^2 - not on our list

b)441 = 21^2 on our list

c)625 =25^2 noton our list

d)729 = on our list but ruled out beacuse of same digits

Hence B

Hope this helps!!
@kvcpk

Slight confusion here, we know pr*qr = sss and we also know that units digit r^2 should not be equal to r and should be equal to s (different from r). If we take, pr = 21, then pr^2 = 441 and we know for a fact that r^2 should end in s which should not be same as r, whereas here it is.

In fact the only number that has a different units digit in the square and the number is 27, hence I have to go with D..........

Thoughts?
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by Stuart@KaplanGMAT » Sun Jul 04, 2010 9:16 am
winnerhere wrote:Each of the letters P,Q,R and S represent a non equal digit.

Q > P and PR x QR = SSS . Then (PR)^2 =

a)676

b)441

c)625

d)729
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by kvcpk » Sun Jul 04, 2010 10:00 am
mj78ind wrote:@kvcpk

Slight confusion here, we know pr*qr = sss and we also know that units digit r^2 should not be equal to r and should be equal to s (different from r). If we take, pr = 21, then pr^2 = 441 and we know for a fact that r^2 should end in s which should not be same as r, whereas here it is.

In fact the only number that has a different units digit in the square and the number is 27, hence I have to go with D..........

Thoughts?
Hi,

The confusion you have is fortunately a simple one..

pr*qr is not equal to pqr^2 because we are not multiplying the digits.
pr in itself is a complete number. same is qr
suppose p=3 and r=2
then pr = 32 not 6.

I hope this helps!!
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by mj78ind » Sun Jul 04, 2010 6:29 pm
kvcpk wrote:
mj78ind wrote:@kvcpk

Slight confusion here, we know pr*qr = sss and we also know that units digit r^2 should not be equal to r and should be equal to s (different from r). If we take, pr = 21, then pr^2 = 441 and we know for a fact that r^2 should end in s which should not be same as r, whereas here it is.

In fact the only number that has a different units digit in the square and the number is 27, hence I have to go with D..........

Thoughts?
Hi,

The confusion you have is fortunately a simple one..

pr*qr is not equal to pqr^2 because we are not multiplying the digits.
pr in itself is a complete number. same is qr
suppose p=3 and r=2
then pr = 32 not 6.

I hope this helps!!
Ok may be I am a bit thick here. Let us say pr = 23, qr = 43. Now the units digit of pr*qr is the same as the units digit of r^2, which in this case is 9. We also know that the units digit of pr*qr is s, we also know that there are certain digits like 1, 5, 6 which have their square's units digits as themselves. Given that p,q,r and s are different the units digit of pr^2 can not equal the units digit of r^2. For example 21, 36 or 45, thus pr can not be a number ending in any one of these digits, now let us look at the choices:
a. 26^2
b. 21^2
c. 25^2
d. 27^2

If we take pr = 26, then pr^2 = 676 which can not be true since the units digit of pr^2 should be different from r (so as to get an s in the unit's digit, we have been told no digits are the same).
Similar logic goes for 21 and 25. Thus the only number left is 27 Hence D
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by kvcpk » Sun Jul 04, 2010 8:05 pm
mj78ind wrote:
kvcpk wrote:
mj78ind wrote:@kvcpk

Slight confusion here, we know pr*qr = sss and we also know that units digit r^2 should not be equal to r and should be equal to s (different from r). If we take, pr = 21, then pr^2 = 441 and we know for a fact that r^2 should end in s which should not be same as r, whereas here it is.

In fact the only number that has a different units digit in the square and the number is 27, hence I have to go with D..........

Thoughts?
Hi,

The confusion you have is fortunately a simple one..

pr*qr is not equal to pqr^2 because we are not multiplying the digits.
pr in itself is a complete number. same is qr
suppose p=3 and r=2
then pr = 32 not 6.

I hope this helps!!
Ok may be I am a bit thick here. Let us say pr = 23, qr = 43. Now the units digit of pr*qr is the same as the units digit of r^2, which in this case is 9. We also know that the units digit of pr*qr is s, we also know that there are certain digits like 1, 5, 6 which have their square's units digits as themselves. Given that p,q,r and s are different the units digit of pr^2 can not equal the units digit of r^2. For example 21, 36 or 45, thus pr can not be a number ending in any one of these digits, now let us look at the choices:
a. 26^2
b. 21^2
c. 25^2
d. 27^2

If we take pr = 26, then pr^2 = 676 which can not be true since the units digit of pr^2 should be different from r (so as to get an s in the unit's digit, we have been told no digits are the same).
Similar logic goes for 21 and 25. Thus the only number left is 27 Hence D
I am sorry.. I think you are right.. I missed looking at the common R in both PR and QR.. R is common..
I was thinking that all 4 are different..
So now, as per my list above, only 37*27 matches - so the answer should be 27^2

Thanks for correcting me..
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