XAT 2014 — QA & DI Question 2
Simple EquationsEasy
In quadrilateral PQRS, PQ = 5 units, QR = 17 units, RS = 5 units, and PS = 9 units. The length of the diagonal QS can be:
Answer & solution
- A
> 10 and < 12
> 12 and < 14
- C
> 14 and < 16
- D
> 16 and < 18
- E
cannot be determined
Solution
Let QS = x, we get the following figure
âââââââ
In any triangle, the sum of any two sides must be greater than the third side. Similarly, the difference between any two sides must be smaller than the third side. Hence,
In âQRS,
x + 5 > 17
⇒ x > 12 …(i)
In âPQS,
x < 9 + 5
⇒ x < 14 …(ii)
Combining (i) and (ii), we get
12 < x < 14
Hence, option (b).