A three digit number abc is such that (i) its hundreds digit is equal to the sum of the other two digits, and (ii) b(c + 1) = 52 - 4a Number of such numbers are

Question

A three digit number abc is such that (i) its hundreds digit is equal to the sum of the other two digits, and (ii) b(c + 1) = 52 - 4a Number of such numbers are (A) 2 (B) 3 (C) 4 (D) 5

Tardigrade Admin · Accepted Answer

N = abc a = b + c b(c + 1) = 52 - 4a b(c + 1) = 52 - 4(b + c) bc + b = 52 - 4b - 4c bc + 5b + 4c + 20 = 52 + 20 (add 20 on both sides) (b + 4)(c + 5) = 72

Q. A three digit number abc is such that
(i) its hundreds digit is equal to the sum of the other two digits, and
(ii) $b (c + 1) = 52 - 4 a$
Number of such numbers are

2

3

4

5

$N = ab c$
$a = b + c$
$b (c + 1) = 52 - 4 a$
$b (c + 1) = 52 - 4 (b + c)$
$b c + b = 52 - 4 b - 4 c$
$b c + 5 b + 4 c + 20 = 52 + 20$ (add 20 on both sides)
$(b + 4) (c + 5) = 72$

Q. A three digit number abc is such that (i) its hundreds digit is equal to the sum of the other two digits, and (ii) b(c+1)=52−4a Number of such numbers are

2

3

4

5

N=abc a=b+c b(c+1)=52−4a b(c+1)=52−4(b+c) bc+b=52−4b−4c bc+5b+4c+20=52+20 (add 20 on both sides) (b+4)(c+5)=72

Q. A three digit number abc is such that
(i) its hundreds digit is equal to the sum of the other two digits, and
(ii) $b (c + 1) = 52 - 4 a$
Number of such numbers are

$N = ab c$
$a = b + c$
$b (c + 1) = 52 - 4 a$
$b (c + 1) = 52 - 4 (b + c)$
$b c + b = 52 - 4 b - 4 c$
$b c + 5 b + 4 c + 20 = 52 + 20$ (add 20 on both sides)
$(b + 4) (c + 5) = 72$