Question

Three children, Ashu, Yacob, and Safina who stay in an orphanage in Bangalore get apples for Christmas. each gets at least one apple. Safina has more apples than Yacob, who has more than Ashu. Together, the total number of apples the three people have is 12. How many apples does Yacob have?
(1) Safina has no more than 5 apples more than Ashu.

(2) The product of the numbers of apples that Ashu, Yacob, and Safina have is less than 36.

• A. IF statement (1) alone is sufficient, but statement (2) is not or If Statement (2) alone is sufficient but statement (1) is not
• B. If Both statements TOGETHER are sufficient, but neither statement ALONE is sufficient
• C. If Each statement ALONE is sufficient
• D. Statement s (1) and (2) TOGETHER are not sufficient

Answer 1

The correct option is B If Both statements TOGETHER are sufficient, but neither statement ALONE is sufficient

x $\to$ number of apples Ashu has
y $\to$ number of apples Yacob has
z $\to$ number of apples Safina has
$x<y<z$
x + y + z = 12
$\begin{array}{cccc}Cases& x& y& z\\ \left(a\right)& 1& 2& 9\\ \left(b\right)& 1& 3& 8\\ \left(c\right)& 1& 4& 7\\ \left(d\right)& 1& 5& 6\\ \left(e\right)& 2& 3& 7\\ \left(f\right)& 2& 4& 6\\ \left(g\right)& 3& 4& 5\end{array}$

Statement (1): INSUFFICIENT. We are told that z - x is less than or equal to 5. This rules out scenarios (a) through (c), but the last four scenarios still work. Thus, y could be 3, 4, or 5.
Statement (2): INSUFFICIENT. We are told that xyz is less than 36. y could be 2, 3, 4, or 5.
Statements (1) and (2) together: SUFFICIENT. Only scenario (d) survives the constraints of the two statements. Thus, we know that y is 5.
The correct answer is (B): BOTH statements TOGETHER are sufficient to answer the question, but neither statement alone is sufficient.