SSAT Math Question 258: Answer and Explanation
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Question: 258
2. In the addition of the three-digit numbers shown, the letters W, X, Y, and Z each represent a unique single digit. Which of the following could be the sum of W + X + Y + Z?
- A. 23
- B. 20
- C. 17
- D. 14
Correct Answer: C
Explanation:
The answer is C
This question requires you to guess and check. Begin with the units digit. Z can be 1 or 6, as 1 + 1 = 2, and 6 + 6 = 12. 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 Z is 6. Now, X can be 2 or 7, as 2 + 2 + 1 = 5, and 7 + 7 + 1 = 15. Finally go to the hundreds digit. W + Y can be any combination that adds up to 9 if X = 2. W + Y can be any combination that adds up to 8 if X = 7, and the 1 was carried. So, the two sets of numbers are (1) Z = 6, X = 2, and W + Y = 9, and (2) Z = 6, X = 7, and W + Y = 8. Thus, the two possible sums of digits are 17 and 21. Only 17 is an answer.