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01 Sep 2022, 05:12
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
56% (02:25) correct
44%
(02:55)
wrong
based on 153
sessions
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'PQ' represents a two digit number. What is the remainder when PQ is divided by 3?
(a) P*Q = 18
(b) P+2 leaves a remainder 1 when divided by 3 and Q+1 leaves a remainder 2 when divided by 3
(a) P*Q = 18
(b) P+2 leaves a remainder 1 when divided by 3 and Q+1 leaves a remainder 2 when divided by 3
01 Sep 2022, 09:49
Kudos
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'PQ' represents a two digit number. What is the remainder when PQ is divided by 3?
(a) P*Q = 18 =2*9 = 3*6
So, PQ could be 36 or 63, then remainder is 0, but when PQ is 29 or 92, then remainder is 2.
Insufficient
(b) P+2 leaves a remainder 1 when divided by 3 and Q+1 leaves a remainder 2 when divided by 3
If P+2 leaves a remainder 1, then P will leave a remainder 3+1-2 or 2.
In other words, (P+2-1) or P+1 is divisible by 3, and P will leave a remainder of 2.
Also, if Q+1 leaves a remainder 2, then Q will leave a remainder 3+2-1 or 4 or 1.
In other words, (Q+1)-2 or Q-1 is divisible by 3, and Q will leave a remainder of 1.
Thus, P+Q will leave a combined remainder of 2+1 or 3, meaning PQ is divisible by 3.
Sufficient
B
(a) P*Q = 18 =2*9 = 3*6
So, PQ could be 36 or 63, then remainder is 0, but when PQ is 29 or 92, then remainder is 2.
Insufficient
(b) P+2 leaves a remainder 1 when divided by 3 and Q+1 leaves a remainder 2 when divided by 3
If P+2 leaves a remainder 1, then P will leave a remainder 3+1-2 or 2.
In other words, (P+2-1) or P+1 is divisible by 3, and P will leave a remainder of 2.
Also, if Q+1 leaves a remainder 2, then Q will leave a remainder 3+2-1 or 4 or 1.
In other words, (Q+1)-2 or Q-1 is divisible by 3, and Q will leave a remainder of 1.
Thus, P+Q will leave a combined remainder of 2+1 or 3, meaning PQ is divisible by 3.
Sufficient
B
01 Sep 2022, 23:30
Kudos
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Gmanimesh
Solution:
We are asked the remainder when a two-digit number PQ is divided by 3
Statement 1: P*Q = 18
The product of the two digits is 18 means they can be 2 and 9 or 3 and 6. So, the two-digit number PQ can be 29, 92, 36 or 63
\((\frac{29}{3})_R=(\frac{92}{3})_R=2\)
and \((\frac{36}{3})_R=(\frac{63}{3})_R=0\)
We are getting 2 different remainders. Thus, statement 1 alone is not sufficient and we can eliminate options A and D
Statement 2: P+2 leaves a remainder 1 when divided by 3 and Q+1 leaves a remainder 2 when divided by 3
According to this statement,
\(P+2=3k_1+1\)
\(⇒P=3k_1+1-2\)
\(⇒P=3k_1-1\)
\(⇒P=3k_1-3+2\)
\(⇒P=3(k_1-1)+2\)
And \(Q+1=3k_2+2\)
\(⇒Q=3k_2+2-1\)
\(⇒Q=3k_2+1\)
If we find \(P+Q\), we will get \(3(k_1-1)+2+3k_2+1=3(k_1-1+k_2)+3=3(k_1-1+k_2+1)\)
This means P+Q is divisible by 3 and thus PQ will be divisible by 3 and will leave the remainder 0 when divided by 3 i.e., \((\frac{PQ}{3})_R=0\)
Thus, statement 2 alone is sufficient
Hence the right answer is Option B
