yass20015 wrote:The integers r, s and t all have the same remainder when divided by 5. What is the value of t ?

1) r+s=t
2) 20 ≤ t ≤ 24

Since r, s, and t all have a remainder of R when divided by 5, they must ALL be contained in ONE of the following lists:
Case 1: R=0
0, 5, 10, 15, 20, 25...
Case 2: R=1
1, 6, 11, 16, 21, 26...
Case 3: R=2
2, 7, 12, 17, 22, 27...
Case 4: R=3
3, 8, 13, 18, 23, 28...
Case 5: R=4
4, 9, 14, 19, 24, 29...

Statement 1: r+s = t
Only Case 1 is viable.
No combination of values from the remaining cases will satisfy the constraint that r+s = t.
In Case 1, it's possible that r=5. s=5, and t=10.
In Case 1, it's possible that r=5, s=10, and t=15.
Since t can take on different values, INSUFFICIENT.

Statement 2: 20 ≤ t ≤ 24
In Case 1, it's possible that t=20.
In Case 2, it's possible that t=21.
Since t can take on different values, INSUFFICIENT.

Statements combined:
Only one value in Case 1 satisfies the constraint that t is between 20 and 24, inclusive: t=20.
SUFFICIENT.

The correct answer is C.

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The integers r, s ans t all have the same remainder when divided by 5. What is the value of t ?

1) r+s=t
2) 20 <= t <= 24

In the original condition, we have 3 variables (r,s,t) and 1 equation (that the remain is the same) thus we need 2 more equations to match the number of variables. Since we have 1 in each 1) and 2), C is likely the answer.

In actual calculation, r=s= multiple of 5, and t=20 which makes them unique and thus the conditions are sufficient. Therefore the answer is C



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Let's say that the remainder is x. This means that

r = 5*something + x
s = 5*something else + x
t = 5*something else again + x

We can write this algebraically as

r = 5k + x
s = 5m + x
t = 5n + x

where k, m, and n are integers whose values we don't care about.

S1 tells us that

r + s = t, or
5k + x + 5m + x = 5n + x, or
5*(k + m) + 2x = 5n + x

In other words, 5*(something) + 2x = 5*(something else) = x, which means that 2x and x represent the same remainder! If x = 0, this works, but if x = 1, 2, 3, or 4, it doesn't. (2*1 = remainder 2, 2*2 = remainder 4, 2*3 = remainder 1, and 2*4 = remainder 3.)

So we know that r, s, and t all have remainder 0 when divided by 5; in other words, they're all multiples of 5. This is close, but no cigar: NOT SUFFICIENT.

S2:: By itself, obviously unhelpful.

Together, we know that t is a multiple of 5 between 20 and 24, inclusive, so t must be 20. Sufficient!