GMAT Data Sufficiency Practice Questions

Let there be S Shovels and R rakes.
The wordy question language may then be simplified to reiterate the question as saying:
What is the value of (14S + 9R) ?


STATEMENT (1) alone: A 2 : 3 ratio does not give us a fix on the total number of shovels
and rakes purchased. It merely states the proportion of items that constitutes shovels and
rakes. For instance there can 2 Shovels and 3 Rakes or 4 Shovels and 6 Rakes or 8 Shovels
and 12 Rakes (and so on) in his purchase. Each possibility yields a different value for (14S +
9R). Which is why,

STATEMENT (1) alone - INSUFFICIENT


STATEMENT (2) alone: This statement says S + R = 50. Although this statement gives us a
fix on the total number purchased. It gives no clue as to the individual number of each
contained in the sum total of 50. Like the above explanation, we can have multiple sets of
(S,R) (say (10,40) or (25,25) for instance) values that add up to 50. All those values again
yield different value for (14S + 9R).

STATEMENT (2) alone - INSUFFICIENT


STATEMENT (1) & (2) together: Together we have a fix on both the total number and the
distribution (ratio) of the two items within the total. This is enough to yield a unique value for
both S & R. Alternatively, mathematically this may be seen as being given two equations: (1)
S = (2/3)*R & (2) S + R = 50 to solve for two variables: S & R uniquely. The unique set
(S,R) further yields a unique value of (14S + 9R). hence,

STATEMENT (1) & (2) together - SUFFICIENT

ANSWER – (C).

We need to determine whether y(z + 1) is odd.

Statement (1) alone: y is odd. If z is even, then z + 1 is odd, and y(z + 1) = odd × odd = odd. However, if z is odd, then z + 1 is even, and y(z + 1) = odd × even = even. Since the result could be either odd or even depending on z, Statement (1) alone is NOT sufficient.

Statement (2) alone: z is even, so z + 1 is odd. If y is odd, then y(z + 1) = odd × odd = odd. However, if y is even, then y(z + 1) = even × odd = even. Since the result could be either odd or even depending on y, Statement (2) alone is NOT sufficient.

Statements (1) and (2) together: y is odd (Statement 1) and z is even (Statement 2), which means z + 1 is odd. Therefore, y(z + 1) = odd × odd = odd. This definitively answers the question with YES. Both statements together are SUFFICIENT.

Answer: C

Given that both \(w\) and \(z\) are positive, the question asks whether \(\frac{w}{z} < 1\).

Since both variables are positive, we can cross-multiply without changing the inequality direction. Thus, the question is equivalent to asking: Is \(w < z\)?

Statement (1) alone: This statement directly confirms that \(w < z\), giving a definitive YES answer to the question.
Statement (1) alone is SUFFICIENT.

Statement (2) alone: This statement tells us that \(z < 4\), but provides no information about \(w\). Using test cases:
- If \(w = 8\) and \(z = 2\): \(\frac{w}{z} = 4 > 1\) (NO)
- If \(w = 1\) and \(z = 2\): \(\frac{w}{z} = 0.5 < 1\) (YES)

Since different values yield different answers, Statement (2) alone is NOT SUFFICIENT.

Answer: (A)