Set P consists of the first n positive multiples of 3 and set Q consists of the first m positive multiples of 5. The sum of all the numbers in set P is equal to R and the sum of all the numbers in set Q is equal to S. If m and n are positive integers, is the difference between R and S odd?
(1) m is odd and n is even
(2) m can be expressed in the form of 4x +3 and n can be expressed in the form of 2x, where x is a positive integer
  • a)
    Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
  • b)
    Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
  • c)
    BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
  • d)
    EACH statement ALONE is sufficient to answer the question asked.
  • e)
    Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'E'. Can you explain this answer?

GMAT Question

I did something different. Please tell me where I might have gone wrong.

P = 3,6,9...3n
Q= 5,10,15...5m

R = 3+6+9..3n
= 3(1+2+3..n) = 3*n(n+1)/2

S = 5*m(m+1)/2 .

We have to chk of R- S is odd.
i.e 3*n(n+1)/2 - 5*m(m+1)/2 is Odd.

Now Statement I -- m is odd and n is even.

If m is Odd then m+1 will be Even.
If n is Even n+1 will be Odd.

Therefore m(m+1) will be Odd*Even which is Even.
And n(n+1) will be Even*Odd which is Even.

So both terms will be divisible by 2 hence R-S will be 3 - 5 = -2 which isn't Odd.

Statement 2 says -- m is 4x+3 ( Which is Odd). Hence m+1 will be 4x+4 (Which is Even).
And n is 2x (Which is Even) . Hence n+1 will be 2x+1 ( Which is Odd.

Therefore again, the product will be even as seen in Statement I hence the answer will also be Even.

Therefore we prove that R-S is not Odd from both statement alone.

Is this wrong?

Steps 1 & 2: Understand Question and Draw Inferences
  • Difference of two integers will be odd, only if one of the numbers is odd.
  • Let’s see when R and S will be odd:
    • The even-odd nature of R will depend on the values of n and n + 1. Since n and n+ 1 are consecutive integers, only one of them can be even.
    • Now, in the expression of R as n(n+1) is divided by 2, for R to be even, either of n or n + 1 should be a multiple of 4, i.e. they should be of the form 4k, where k is a positive integer. Hence, following cases arise:
      • n is of the form 4k, i.e. n = 4k OR
      • n+1 is of the form 4k, i.e. n + 1 = 4k
        • So, n = 4k – 1 = 4(k -1) + 4 -3 = 4(k-1) + 3
    • So, we can say that R will be even if n is of the form 4k or 4k + 3. For all the other cases, R will be odd
  • Since the expression of S is similar to R, we can say that S will be even if m is of the form 4k or 4k + 3
  • So, we need to look for values of m and n in the statements.
Step 3: Analyze Statement 1 independently
(1) m is odd and n is even
  • As we do not know if m or n is of the form of 4k or 4k + 3, we cannot say, if R and S are odd or even.
  • Insufficient to answer.
 
Step 4: Analyze Statement 2 independently
(2) m can be expressed in the form of 4x +3 and n can be expressed in the form of 2x, where x is a positive integer
  • As m can be expressed in the form of 4x + 3, S will be even.
  • As n can be expressed in the form of 2x, n may be expressed in the form of 4x or may not be expressed in the form of 4x.
    • So, R may be odd or R may be even.
      • If R is odd,  R – S = odd
      • If R is even, R – S = even.
  • Hence, we cannot say for sure if R – S is odd.
  • Insufficient to answer.
 
Step 5: Analyze Both Statements Together (if needed)
(1) From statement-1, we know that  is odd and n is even
(2) From statement-2, we know that R may be even or odd and S is even
  • Combining both the statements does not tell us anything about the even-odd nature of R, hence we cannot say for sure if R – S = odd.
  • Insufficient to answer.
Answer: E

This discussion on Set P consists of the first n positive multiples of 3 and set Q consists of the first m positive multiples of 5. The sum of all the numbers in set P is equal to R and the sum of all the numbers in set Q is equal to S. If m and n are positive integers, is the difference between R and S odd?(1) m is odd and n is even(2) m can be expressed in the form of 4x +3 and n can be expressed in the form of 2x, where x is a positive integera)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'E'. Can you explain this answer? is done on EduRev Study Group by GMAT Students. The Questions and Answers of Set P consists of the first n positive multiples of 3 and set Q consists of the first m positive multiples of 5. The sum of all the numbers in set P is equal to R and the sum of all the numbers in set Q is equal to S. If m and n are positive integers, is the difference between R and S odd?(1) m is odd and n is even(2) m can be expressed in the form of 4x +3 and n can be expressed in the form of 2x, where x is a positive integera)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'E'. Can you explain this answer? are solved by group of students and teacher of GMAT, which is also the largest student community of GMAT. If the answer is not available please wait for a while and a community member will probably answer this soon. You can study other questions, MCQs, videos and tests for GMAT on EduRev and even discuss your questions like Set P consists of the first n positive multiples of 3 and set Q consists of the first m positive multiples of 5. The sum of all the numbers in set P is equal to R and the sum of all the numbers in set Q is equal to S. If m and n are positive integers, is the difference between R and S odd?(1) m is odd and n is even(2) m can be expressed in the form of 4x +3 and n can be expressed in the form of 2x, where x is a positive integera)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'E'. Can you explain this answer? over here on EduRev! Apart from being the largest GMAT community, EduRev has the largest solved Question bank for GMAT.