Data Sufficiency

BTGmoderatorDC wrote: ↑

Fri May 26, 2023 6:30 pm

Are all of the terms in Set A equal?

(1) The sum of all 14 terms in Set A is 98.
(2) The sum of any 3 terms in Set A is 21.


OA C

Source: Veritas Prep

Target question: Are all of the terms in Set A equal?

Statement 1: The sum of all 14 terms in Set A is 98
There are several possible scenarios that satisfy this statement. Here are two.
Case a: Set A = {7,7,7,7,7,7,7,7,7,7,7,7,7,7} in which case all of the numbers ARE equal
Case b: Set A = {0,0,0,0,0,0,0,0,0,0,0,0,0,98}, in which case all of the numbers are NOT equal
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The sum of any 3 terms in Set A is 21
Under most conditions this statement WOULD be sufficient.
However, if set A has only 3 terms in total, then the statement is NOT sufficient.
To see what I mean, consider these two possible scenarios that satisfy statement 2:
Case a: Set A = {7,7,7} in which case all of the numbers ARE equal
Case b: Set A = {0, 0, 21}, in which case all of the numbers are NOT equal
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
The combined statements ARE sufficient. Here's why:
Let's let a,b,c and d be four of the 14 numbers in set A.
From statement 2, we know that a + b + c = 21
Notice that if I replace ANY of these three values (a,b or c) with d, the sum must still be 21 (according to statement 2)
This tells us that a, b and c must all equal d.
I can use a similar approach to show that all of the other numbers must also equal d.
This means that all of the numbers in set A must be equal.
Since we can answer the target question with certainty, the COMBINED statements are SUFFICIENT

Answer: C

Cheers,
Brent