Question : Directions: In the following question, you have to identify the correct response from the given premises stated according to the following symbols.
If + means division, – means multiplication, ÷ means subtraction, × means addition, and < means less than, then which of the following is false?
Option 1: (10 + 2) ÷ 7 < (10 ÷ 7) + 2
Option 2: (10 – 7) × 2 < (10 × 2) – 7
Option 3: (10 × 7) – 2 < (10 – 2) × 7
Option 4: (10 ÷ 2) + 7 < (10 ÷ 7) × 2
Correct Answer: (10 × 7) – 2 < (10 – 2) × 7
Solution :
Let's check the options –
First option:
(10 + 2) ÷ 7 < (10 ÷ 7) + 2
On replacing with symbols as directed, we get –
(10 ÷ 2) – 7 < (10 – 7) ÷ 2
L.H.S.→(10 ÷ 2) – 7 = 5 – 7 = – 2
R.H.S.→(10 – 7) ÷ 2 = 3 ÷ 2 = 1.5
L.H.S. < R.H.S.
Second option:
(10 – 7) × 2 < (10 × 2) – 7
On replacing with symbols as directed, we get –
(10 × 7) + 2 < (10 + 2) × 7
L.H.S.→(10 × 7) + 2 = 70 + 2 = 72
R.H.S.→(10 + 2) × 7 = 12 × 7 = 84
L.H.S. < R.H.S.
Third option:
(10 × 7) – 2 < (10 – 2) × 7
On replacing with symbols as directed, we get –
(10 + 7) × 2 < (10 × 2) + 7
L.H.S.→(10 + 7) × 2 = 17 × 2 = 34
R.H.S.→(10 × 2) + 7 = 20 + 7 = 27
L.H.S. > R.H.S.
Fourth option:
(10 ÷ 2) + 7 < (10 ÷ 7) × 2
On replacing with symbols as directed, we get –
(10 – 2) ÷ 7 < (10 – 7) + 2
L.H.S.→(10 – 2) ÷ 7 = 8 ÷ 7 = 1.14
R.H.S.→(10 – 7) + 2 = 3 + 2 = 5
L.H.S. < R.H.S.
So, only the third option does not satisfy the equation. Hence, the third option is correct.
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