ABC26GN1723 · Problems on Numbers

Subject: General Aptitude · Chapter: Problems on Numbers · Exam: 2003 · Marks: · Difficulty:

What is the sum of two consecutive even numbers, the difference of whose squares is 84?
(a)34
(b)38
(c)42
(d)46
Answer
Answer (as printed): C
Explanation
Let the numbers be $x$ and $x+2$. Then, $(x+2)^{2}-x^{2}=84$ $$\begin{array}{ll} \Leftrightarrow & 4 x+4=84 \\ \Leftrightarrow & 4 x=80 \\ \Leftrightarrow & x=20 . \\ \therefore & \text { Required sum }=x+(x+2)=2 x+2=42 . \end{array}$$

Explanation as extracted from the printed page; notation may be imperfect.

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