If ‘×’ stands for addition, ‘<’ stands for subtraction, ‘+’ stands for division, ‘>’ stands for multiplication, ‘–’ stands for equal, ‘÷’ stands for greater than, and ‘=’ stands for less than. State which of the following is true ?
1) 3 × 2 < 4 ÷ 16 > 2 + 4
2) 5 > 8 + 4 = 10 < 4 × 8
3) 3 × 4 > 2 – 9 + 3 < 3
4) 5 × 3 < 3 ÷ 8 + 4 + 1
Answer & explanation
Correct answer: option 3
from (1)
3 × 2 < 4 ÷ 16 > 2 + 4
⇒ 3 + 2 – 4 > 16 × 2 ÷ 4
⇒ 5 – 4 > \(\frac{16 × 2}{4}\) ⇒ 1 > 8 (not possible)
from (2)
5 > 8 + 4 = 10 < 4 × 8
⇒ 5 × 8 ÷ 4 < 10 – 4 + 8
⇒ 5 × 2 < 18 – 4
⇒ 10 < 14
from (3)
3 × 4 > 2 – 9 + 3 < 3
⇒ 3 + 4 × 2 = 9 ÷ 3 – 3
⇒ 3 + 8 = 3 – 3
⇒ 11 = 0 (not possible)
from (4)
5 × 3 < 3 ÷ 8 + 4 + 1
⇒ 5 + 3 – 3 > 8 ÷ 4 ÷ 1
⇒ 8 – 3 > 2 ÷ 1
⇒ 5 > 2
Both (2) and (4) are correct.