Question 1

When 1/7 of a number is subtracted from the number itself, it gives the same value as the sum of all the angels of a triangle. What is the number?

Accepted Answer

Let the number be P. According to the question, P - P/7 = 180 ⇒ 6P/7 = 180 ∴ P = 180 x 7/6 = 210

Question 2

In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 46, then find the dividend?

Accepted Answer

Divisor = 5 x 46 = 230 Also, 10 x Quotient = 230 ∴ Quotient = 23 We know that Dividend = (Divisor x Quotient ) + Remainder ∴ Dividend = (230 x 23) + 46 ∴ Dividend = 5290 + 46 = 5336

Question 3

The product of two consecutive odd number is 6723. What is the greater number?

Accepted Answer

Let two consecutive odd number be (A + 1) and (A + 3). According to the question. (A + 1) (A + 3) = 6723 ⇒ A2 + 3A + A + 3 = 6723 ⇒ A2 + 4A + 3 - 6723 = 0 ⇒ A2 + 4A - 6720 = 0 ⇒ A2 + 84A - 80A - 6720 = 0 ⇒ A(A + 84) - 80 (A + 84) = 0 ⇒ (A - 80) (A + 84) = 0 ∴ A = 80, (A = ≠ - 84) Hence, the greater number = 80 + 3 = 83

Question 4

The sum of the four consecutive even numbers is 284. What would be the smallest number.

Accepted Answer

Let four consecutive even numbers are P, P + 2, P + 4 and P + 6 According to the question, P + P + 2 + P + 4 + P + 6 = 284 ⇒ 4P + 12 = 284 ⇒ 4P = 284 - 12 = 272 ∴ P = 272/4 = 68

Question 5

The sum of the digits of a two-digit number is 14 and the difference between the two digits of the number is 2. What is the product of the two digits of the two-digit number?

Accepted Answer

Let be the ten's digit be P and unit's digit be Q. The two-digit number = 10P + Q (where, P > Q) According to the question, P + Q = 14 ......(i) and P - Q = 2 .......(ii) solving Eqs. (i) and (ii), we get P = 8 and Q = 6 ∴ Required product = 8 x 6 = 48

Number System Questions