Discussion Forum



Each of the questions given below consists of a statement and/ or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is / are sufficient to answer the given question.

  • Mark answer (A) if (I) alone sufficient while (II) alone not sufficient to answer
  • Mark answer (B) if (II) alone sufficient while (I) alone not sufficient to answer.
  • Mark answer (C) if Either (I) or (II) alone sufficient to answer.
  • Mark answer (D) Both (I) and (II) are not sufficient to answer.
  • Mark answer (E) Both (I) and (II) are necessary to answer.
1)

What is the average age of X and Y?

I) The ratio between one-fifth of X's age and one-fourth of Y's age is $1:2$
II) The product of their ages is 20 times Y's age.


A) I) alone sufficient while II) alone not sufficient

B) II) alone sufficient while I) alone not sufficient

C) Either I) or II) alone sufficient

D) Both I) and II) are not sufficient

E) Both I) and II) are necessary

Answer:

Option E

Explanation:

I) $\frac{X}{5}:\frac{Y}{4}=1:2$
$\Leftrightarrow \frac{X}{5} \times \frac{4}{Y}$ $=\frac{1}{2}$
$\Leftrightarrow \frac{X}{Y}$
$=\left(\frac{1}{2}\times\frac{5}{4}\right)$
$=\frac{5}{8}$
$\Leftrightarrow X:Y = 5:8$

II) $20Y = XY$
Let X's age be $5x$ years. Then Y's age is $8x$ years.
$\therefore$ $20 \times 8x$
$=5x \times 8x$ $\Leftrightarrow 40x = 160$
$\Leftrightarrow x =4$.
$\therefore$ $X = 20$ and $Y = 32$.
Thus, I and II together give the answer. So, correct answer is (E)