Two consecutive positive integers, each greater than 9, are divided by 5. What is the sum of the remainders?
(1) The sum of the remainders is even.
(2) The sum of the units digits of the two original integers is 9.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
Before analyzing the statements, it is helpful to test a few numbers to see whether there is a pattern (there usually is!). Each of the integers is 10 or greater. If 10 is divided by 5, the remainder is 0. Continue to find the pattern:
#
Remainder
10/5
0
11/5
1
12/5
2
13/5
3
14/5
4
15/5
1
16/5
0
The pattern, then, is 0, 1, 2, 3, 4 repeating.
(1) SUFFICIENT: Given the pattern above and the fact that the two numbers must be consecutive, there are only five possible sums for the remainder:
0 + 1 = 1
1 + 2 = 3
2 + 3 = 5
3 + 4 = 7
4 + 0 = 4
Of these, 4 is the only even sum, so the answer to the question must be 4.
STATEMENT (2) SUFFICIENT: The two integers must be consecutive, so the two must have units digits of either 4 and 5 (14 and 15, 24 and 25, and so on) or 9 and 0 (19 and 20, 29 and 30, and so on) Test both cases. The sum of the remainders for two numbers with units digits of 4 and 5 must be 4+0 = 4 (use the values of 14 and 15 in the table above to test this!). If the units digits are 9 and 0 (for example, 19 and 20), then the two remainders are also 4 and 0, for a sum of 4. In either case, the sum of the remainders must be 4 + 0 = 4.
The correct answer is D.
Didn't know if you guys cared; however, thought it would be worth sharing incase you do want to change it! Thanks for your time
.
(1) The sum of the remainders is even.
(2) The sum of the units digits of the two original integers is 9.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
Before analyzing the statements, it is helpful to test a few numbers to see whether there is a pattern (there usually is!). Each of the integers is 10 or greater. If 10 is divided by 5, the remainder is 0. Continue to find the pattern:
#
Remainder
10/5
0
11/5
1
12/5
2
13/5
3
14/5
4
15/5
1
16/5
0
The pattern, then, is 0, 1, 2, 3, 4 repeating.
(1) SUFFICIENT: Given the pattern above and the fact that the two numbers must be consecutive, there are only five possible sums for the remainder:
0 + 1 = 1
1 + 2 = 3
2 + 3 = 5
3 + 4 = 7
4 + 0 = 4
Of these, 4 is the only even sum, so the answer to the question must be 4.
STATEMENT (2) SUFFICIENT: The two integers must be consecutive, so the two must have units digits of either 4 and 5 (14 and 15, 24 and 25, and so on) or 9 and 0 (19 and 20, 29 and 30, and so on) Test both cases. The sum of the remainders for two numbers with units digits of 4 and 5 must be 4+0 = 4 (use the values of 14 and 15 in the table above to test this!). If the units digits are 9 and 0 (for example, 19 and 20), then the two remainders are also 4 and 0, for a sum of 4. In either case, the sum of the remainders must be 4 + 0 = 4.
The correct answer is D.
Didn't know if you guys cared; however, thought it would be worth sharing incase you do want to change it! Thanks for your time
.
