Explanation

75% had at least one lunch → 25% had none.

25% × 96 = 24 people ate neither.

Explanation

Simplify each term: (2/3 × 45) = 30, 3⅘ = 3.8, 20.

Total = -19.

Explanation

A number divisible by 7, 11 and 13:

= LCM of 7, 11 and 13

= 1001

A number which is multiple of 1001 is of the form:

Xyz xyz …….. (digits repeating)

Answer: 624624

Explanation

Common ratio r = 2.

Sum of 10 terms = 3 × (2¹⁰ - 1) = 3069

Explanation

Each pair (2,5), (4,7), (17,6) has no common factor other than 1.

Hence, they are co-prime (relatively prime) numbers.

Explanation

Total ways = (12 2) = 66; same color ways = 10 + 6 + 3 = 19

Different color ways = 66 - 19 = 47; so probability = 47/66.

Explanation

From DRAIN → ^!#*@, we get the mapping: D→^, R→!, A→#, I→*, N→@.

Encode NARD as N(@) A(#) R(!) D(^) → @#!^.

Explanation

For 123 → 13², the first and last digits 1 and 3 form 13, then squared gives 169.

Apply same rule to 235 → first and last digits 2 and 5 form 25, squared gives 625.

Explanation

The word CHORD has 5 distinct letters: C-H-O-R-D.

When taking all the letters together, the number of ways to arrange them is equal to the number of permutations of 5 items, which is calculated as:

5! = 5 × 4 × 3 × 2 × 1 = 120

Explanation

Letters are replaced by their alphabet positions and concatenated: L(12) M(13) → 1213.

Similarly, C(3) D(4) → 34.