Mathematics MCQs

The least common multiple of 3 and 4 is 12.
A number divisible by both must therefore be divisible by 12.

The score fraction is 42/50.
Multiplying by 100 gives 84%.

The cost per pen is 150 ÷ 5 = Rs. 30.
Eight pens cost 8 × 30 = Rs. 240.

Six consecutive integers centered at 17.5 are 15 through 20.
Therefore, the smallest is 15.

For two years, the difference is P(r/100)².
So 10,000 × 0.1² = Rs. 100.

The units digits of powers of 7 cycle as 7, 9, 3, 1.
The fourth power therefore ends in 1.

Starting from 100, a 10% increase gives 110.
A 10% decrease from 110 gives 99, which is 1% lower.

Workers and time are inversely proportional for fixed work.
Thus, 12 × 15 = 20 × days, giving 9 days.

The average of 1 through n is (n + 1)/2.
Setting (n + 1)/2 = 20 gives n = 39.

Doubling means interest equal to the principal is earned in 8 years.
Tripling requires interest equal to twice the principal, so it takes 16 years.

Since 2 ≡ -1 (mod 3), 2¹⁰ ≡ (-1)¹⁰ = 1.
Therefore, the remainder is 1.

After a 20% increase, the quantity becomes 120% of the original.
The required reduction is 20/120 × 100 = 16⅔%.