SSAT Math Question 406: Answer and Explanation

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Question: 406

17. What could be the sum of M, N, P, and Q if each letter represents a different digit?

  • A. 18
  • B. 17
  • C. 16
  • D. 13

Correct Answer: A

Explanation:

A

This question requires you to guess and check. Begin with the units digit. Q can be 0 or 5, as 0 + 0 = 0, and 5 + 5 = 10. Proceed to the tens digit. There is no number that when added to itself will yield an odd number. Thus, we need to carry a 1 from the sum of the units digit. We now know that Q is 5. Now, N can be 3 or 8, as 3 + 3 + 1 = 7, and 8 + 8 + 1 = 17. Finally go to the hundreds digit. M + P can be any combination that adds up to 6 if N = 3. M + P can be any combination that adds up to 5 if N = 8, and the 1 was carried. So, the two sets of numbers are (1) Q = 5, N = 3, and M + P = 6, and (2) Q = 5, N = 8, and M + P = 5. Thus, the two possible sums of digits are 14 and 18. Only 18 is an answer.

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