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In the correctly worked addition problem shown, P, Q, R, and S are dig
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gmatt1476
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In the correctly worked addition problem shown, P, Q, R, and S are dig [#permalink] New post  Updated on: 02 May 2020, 13:19
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In the correctly worked addition problem shown, P, Q, R, and S are digits. If Q = 2P, which of the following could be the value of S ?

(A) 3
(B) 2
(C) 1
(D) -1
(E) -2

PS07601.02


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Originally posted by gmatt1476 on 20 Apr 2020, 11:13.
Last edited by carcass on 02 May 2020, 13:19, edited 1 time in total.
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sujoykrdatta
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Re: In the correctly worked addition problem shown, P, Q, R, and S are dig [#permalink] New post  20 Apr 2020, 11:58
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gmatt1476 wrote:
3P5
+4QR
_____
8S4

In the correctly worked addition problem shown, P, Q, R, and S are digits. If Q = 2P, which of the following could be the value of S ?

(A) 3
(B) 2
(C) 1
(D) -1
(E) -2

PS07601.02


Units digit: 5 + R results in 4 => The only possible scenario is that R = 9 and 5+R = 14, of which 1 is a carry in the tens position
For the tens place: 1 + P + Q = S (with or w/o a carry)
However, in the hundreds place: 3 + 4 gives 8 => there was a carry of 1
=> In the tens place: 1 + P + Q = S + 10
=> P + Q = S + 9
=> P + 2P = S + 9
=> 3P = S + 9
=> S must be a multiple of 3

=>S = 0 or 3 or 6 or 9

Answer A
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BrentGMATPrepNow
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Re: In the correctly worked addition problem shown, P, Q, R, and S are dig [#permalink] New post  30 Apr 2020, 09:55
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gmatt1476 wrote:
3P5
+4QR
_____
8S4

In the correctly worked addition problem shown, P, Q, R, and S are digits. If Q = 2P, which of the following could be the value of S ?

(A) 3
(B) 2
(C) 1
(D) -1
(E) -2

PS07601.02



We can also solve this question algebraically

Key property: The VALUE of the 3-digit integer abc can be written as follows: abc = 100a + 10b + c
For example: 625 = 100(6) + 10(2) + 5

Likewise: 3P5 = 100(3) + 10(P) + 5, 4QR = 100(4) + 10(Q) + R, and 8S4 = 100(8) + 10(S) + 4

So the addition, 3P5 + 4QR = 8S4 can be written algebraically as: (300 + 10P + 5) + (400 + 10Q + R) = 800 + 10S + 4
Simplify: 705 + 10P + 10Q + R = 804 + 10S
Subtract 705 from both sides to get: 10P + 10Q + R = 99 + 10S
Subtract 10S from both sides: 10P + 10Q - 10S + R = 99
Subtract R from both sides: 10P + 10Q - 10S = 99 - R
Factor the left side: 10(P + Q - S) = 99 - R
Finally, since we're told that Q = 2P, we can substitute to get: 10(P + 2P - S) = 99 - R
Simplify: 10(3P - S) = 99 - R
Since 10(3P - S) is a multiple of 10, and since R is a digit, we know that R must equal 9
We get: 10(3P - S) = 99 - 9 = 90

Now take: 10(3P - S) = 90
Divide both sides by 10 to get: 3P - S = 9
Rearrange to get: S = 3P - 9
Factor to get: S = 3(P - 3)
This means S is a multiple of 3

Check the answer choices..... answer choice A (3) is the only multiple of 3

Answer: A

Cheers,
Brent
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nick1816
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Re: In the correctly worked addition problem shown, P, Q, R, and S are dig [#permalink] New post  20 Apr 2020, 11:31
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3P5 =300+10P+5

03P5
+4QR
_____
08S4

Only value R can take is 9
.+1...+1
03.... P............ 5
+4.....Q........... 9
_______________
8.........S...........4

Hence P+Q+1 = 10+S

3P+1 = 10+S

3P+1-10= S

3(P-3) = S

Hence S must be multiple of 3; S can take only 1 value among all options, that is 3.

A



gmatt1476 wrote:
3P5
+4QR
_____
8S4

In the correctly worked addition problem shown, P, Q, R, and S are digits. If Q = 2P, which of the following could be the value of S ?

(A) 3
(B) 2
(C) 1
(D) -1
(E) -2

PS07601.02
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Re: In the correctly worked addition problem shown, P, Q, R, and S are dig [#permalink] New post  21 Apr 2020, 10:00
3P5
+4QR
8S4
5+r = 4 ;only possible when r = 9
given that Q=2P
and hundereds digit is 8 ; so we have +1 carry fwd from tens place
which means that P+Q+1= S+10
+1 on LHS is carry fwd from units place of 5+9 ; 14

3Q=S+9
S has to be 0,3,6,9
from given options S = 3 sufficient
OPTION A


gmatt1476 wrote:
3P5
+4QR
_____
8S4

In the correctly worked addition problem shown, P, Q, R, and S are digits. If Q = 2P, which of the following could be the value of S ?

(A) 3
(B) 2
(C) 1
(D) -1
(E) -2

PS07601.02
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rahulbhusan
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Re: In the correctly worked addition problem shown, P, Q, R, and S are dig [#permalink] New post  22 Apr 2020, 05:48
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gmatt1476 wrote:
3P5
+4QR
_____
8S4

In the correctly worked addition problem shown, P, Q, R, and S are digits. If Q = 2P, which of the following could be the value of S ?

(A) 3
(B) 2
(C) 1
(D) -1
(E) -2

PS07601.02


3P5
+4QR
_____
8S4

We can easily deduce that the value of R will be 9, such that total becomes 5+9= 14
so, 1+P+Q= S [ 1, because of the carry from 14]
Given , Q=2P
so, 1+P+2P= S
=> S= 3P+1
We, see that the hundred's digit is 8, so we need to get a carry of 1 from the addition of 3P+1
Maximum value of P can be 4 and minimum value can be 3 [As Q=2P, and 1+Q+P>=10]
So, value of S can be either '0'(when, P=3) or '3' (when P=4)
from the options 3 fits the bill.
(Option A)
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Re: In the correctly worked addition problem shown, P, Q, R, and S are dig [#permalink] New post  26 Apr 2020, 12:03
2
Kudos
gmatt1476 wrote:
3P5
+4QR
_____
8S4

In the correctly worked addition problem shown, P, Q, R, and S are digits. If Q = 2P, which of the following could be the value of S ?

(A) 3
(B) 2
(C) 1
(D) -1
(E) -2

PS07601.02


R must be 9 because the units digit of the sum, 5 + R, is 4.

3P5 + 4Q9 = 8S4

305 + 10P +409 + 10Q = 804 +10S

Since Q = 2P,

714 + 30P = 804 + 10S

30P - 90 = 10S

3P - 9 = S

S = 3(P - 3)

We can see that S must be divisible by 3, and there is only one answer choice divisible by 3.

Answer: A
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Re: In the correctly worked addition problem shown, P, Q, R, and S are dig [#permalink] New post  26 May 2020, 01:41
My possible answer options are different with what is posted here.

A. 3
B. 4
C. 5
D. 7
E. 9
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perfectreview
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Re: In the correctly worked addition problem shown, P, Q, R, and S are dig [#permalink] New post  31 May 2020, 08:33
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By looking at the options we can eliminate options D and E

from the question we can say

5 + R = 4, this happens of if R is 9

If R = 9, then there is a carry forward to the \(2^{nd}\) line.

in the third line we have 3 + 4 = 8, this happens only if there is a carry forward to the \(3^{nd}\) line from the \(2^{nd}\) line.

If there should be a carry forward from the second line then the value of P has to be either 3 or 4.

Since we know Q = 2P

If P = 3 then Q = 6 then P + Q + 1 = 3 + 6 + 1 = 10
so the possible value of S = 0

If P = 4 then Q = 8 then P + Q + 1 = 4 + 8 + 1 = 13
so the possible value of S = 3

Now the possible values of S are 0 or 3

According to the options the answer has to be Option A
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Re: In the correctly worked addition problem shown, P, Q, R, and S are dig [#permalink] New post  25 May 2021, 06:12
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gmatt1476 wrote:
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In the correctly worked addition problem shown, P, Q, R, and S are digits. If Q = 2P, which of the following could be the value of S ?

(A) 3
(B) 2
(C) 1
(D) -1
(E) -2

PS07601.02


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Re: In the correctly worked addition problem shown, P, Q, R, and S are dig [#permalink] New post  25 May 2021, 10:20
I followed a very simple method:

S cannot be a number greater than 10 (i.e) it has to be between 0 and 9.

We have P. We have Q=2P. We know that P+Q=S. We also know that S<=9

Therefore,

P + Q <= 9
P+2P <= 9
3P <= 9
P <= 3

Therefore we have the following possibilities for P, Q, and S

P: 0 | 1 | 2 | 3
Q: 0 | 2 | 4 | 6
S: 0 | 3 | 6 | 9

3 is the only option in the answer choices. Answer is (A)
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Re: In the correctly worked addition problem shown, P, Q, R, and S are dig [#permalink]
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