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Difficulty:
45%
(medium)
Question Stats:
59% (01:26) correct
41%
(01:20)
wrong
based on 27
sessions
History
Date
Time
Result
Not Attempted Yet
What is the product of positive integers P and Q?
(1) 18P + Q = 367
(2) Q < 18
(1) 18P + Q = 367
(2) Q < 18
14 Apr 2022, 10:58
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Step 1: Analyse Question Stem
P and Q are positive integers. The product of P and Q is to be calculated.
We will need unique values of P & Q to be able to do that.
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1: 18P + Q = 367
We have one linear equation in 2 unknowns. Although we have a constraint on P and Q that they have to be positive integers, there can be more than 1 value for each of them.
Dividing both sides of the equation by 18, we have,
P + \(\frac{Q }{18}\) = \(\frac{360 }{ 18} + \frac{7 }{ 18}\).
P + \(\frac{Q }{18}\) = 20 +\( \frac{7 }{ 18}\).
Transferring the \(\frac{Q }{ 18}\) to the RHS, we have,
P = 20 +\( \frac{(7 – Q) }{18}\).
Now, for P to be a positive integer, (7 – Q) should be a multiple of 18.
The first value of Q can be 7; (7-7) = 0 which is a multiple of 18. The corresponding value of P is 20.
Note: 0 is a multiple of all numbers.
To obtain the next value of Q, we add the coefficient of P to the first value of Q. Therefore, the next value of Q = 25 and corresponding value of P = 19.
The next value of Q = 25 + 18 = 43 and corresponding value of P = 19 – 1 = 18.
Thus, solving special linear equations involves rearranging the terms, finding out the first set of values of the variables and then changing each of the variables by the coefficient of the other.
It’s clear from the above analysis that there are multiple possible values for P and Q and hence multiple possible values for their product.
Statement 1 alone is insufficient. Answer options A and D can be eliminated.
Statement 2: Q < 18
We have no information about P. Hence, we cannot find the value of the product of P and Q.
Statement 2 alone is insufficient. Answer option B can be eliminated.
Step 3: Analyse Statements by combining
From statement 1: Q = 7 and P = 20; Q = 25 and P =19; Q = 43 and P = 18 and so on.
From statement 2: Q < 18
Therefore, the only set of values that satisfy both the constraints is Q = 7 and P = 20.
P * Q = 140.
The combination of statements is sufficient. Answer option E can be eliminated.
The correct answer option is C.
P and Q are positive integers. The product of P and Q is to be calculated.
We will need unique values of P & Q to be able to do that.
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1: 18P + Q = 367
We have one linear equation in 2 unknowns. Although we have a constraint on P and Q that they have to be positive integers, there can be more than 1 value for each of them.
Dividing both sides of the equation by 18, we have,
P + \(\frac{Q }{18}\) = \(\frac{360 }{ 18} + \frac{7 }{ 18}\).
P + \(\frac{Q }{18}\) = 20 +\( \frac{7 }{ 18}\).
Transferring the \(\frac{Q }{ 18}\) to the RHS, we have,
P = 20 +\( \frac{(7 – Q) }{18}\).
Now, for P to be a positive integer, (7 – Q) should be a multiple of 18.
The first value of Q can be 7; (7-7) = 0 which is a multiple of 18. The corresponding value of P is 20.
Note: 0 is a multiple of all numbers.
To obtain the next value of Q, we add the coefficient of P to the first value of Q. Therefore, the next value of Q = 25 and corresponding value of P = 19.
The next value of Q = 25 + 18 = 43 and corresponding value of P = 19 – 1 = 18.
Thus, solving special linear equations involves rearranging the terms, finding out the first set of values of the variables and then changing each of the variables by the coefficient of the other.
It’s clear from the above analysis that there are multiple possible values for P and Q and hence multiple possible values for their product.
Statement 1 alone is insufficient. Answer options A and D can be eliminated.
Statement 2: Q < 18
We have no information about P. Hence, we cannot find the value of the product of P and Q.
Statement 2 alone is insufficient. Answer option B can be eliminated.
Step 3: Analyse Statements by combining
From statement 1: Q = 7 and P = 20; Q = 25 and P =19; Q = 43 and P = 18 and so on.
From statement 2: Q < 18
Therefore, the only set of values that satisfy both the constraints is Q = 7 and P = 20.
P * Q = 140.
The combination of statements is sufficient. Answer option E can be eliminated.
The correct answer option is C.
14 Apr 2022, 11:02
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Bunuel
What is the product of positive integers P and Q?
(1) 18P + Q = 367
(2) Q < 18
(1) 18P + Q = 367
(2) Q < 18
Statement 1 - Multiple values of P and Q are possible which will give different values of P * Q
Not sufficient
Statement 2 - Nothing mentioned about P
Not sufficient
Combing both,
Smallest value of Q = 7, P = 20 in such case
Next value of Q will be 25 which is greater than 18.
Unique value of P and Q
Sufficient
Option C
