Did David solve more questions than Steve in ...

### Related Test

Did David solve more questions than Steve in a 2-hour test?
(1) Thrice the number of questions that David solved in the test was greater than 6 less than thrice the number of questions that Steve solved in the test.
(2) Twice the number of questions that David solved in the test was greater than 4 less than twice the number of questions that Steve solved in the test.
• a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;
• b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;
• c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;
• d)
• e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Statement 1:
We are given that Thrice the number of questions that David solved in the test was greater than 6 less than thrice the number of questions that Steve solved in the test.
⇒ 3x > 3y − 6
⇒ x > y − 2
We cannot determine whether x > y, since x is greater than a quantity y, which is reduced by a certain amount, 2.
Let us take an example.
Say y = 10, thus x > 10−2 ⇒ x > 8.
If x = 9, then x ≯ y and the answer is No. However, if x = 11, then x > y and the answer is Yes. No unique answer. Insufficient!
Statement 2:
We are given that Twice the number of questions that David solved in the test was greater than 4 less than twice the number of questions that Steve solved in the test.
⇒ 2x > 2y − 4
⇒ x > y − 2
This is the same inequality that we got in Statement 1. Insufficient!
Statement 1 & 2:
Since each statement renders the same inequality, even combining both the statements cannot help. Insufficient!
Conclusion:
Each statement renders that same inequality, thus combining both the statements will not help.
You may have deduced a wrong conclusion with the inequality x > y − 2.
We see that x is greater than a number y minus 2; thus, x may or may not be greater than y.
Had the situation been x > y + 2, then it's for certain that x > y; since x is greater than a number (y + 2), then x must be greater than a relatively smaller number y.

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