mahts

1.

When a number x is increased by 10%, the new value will be (1+10%) x = 1.1x

When a number y is decreased by 10%, the new value will be (1-10%) y = 0.9y

So when a number x is increased by 10% then decreased by 10%, the new value should be (1+10%) (1-10%) x = 1.1 * 0.9 x = 0.99x

The correct answer should be decreased by 1% instead of no change.



2.

Let the ten-digit be x and the unit-digit be y.

x = y + 2 ………….equation 1
y ^2 > 2x => y^2 – 2x > 0 …………….equation 2

Let’s substitute equation 1 into equation 2

y^2 – 2(y+2) > 0
y^2 – 2y – 4 > 0 …………..equation 3

From the question we know that both x and y are within the range 1 to 9. Since x = y + 2, so x must be in the range 3 to 9 while y must be in the range 1 to 7.

By substituting various value of y in the range 1 to 7 into equation 3, we note that

When y = 4, y^2 – 2y – 4 = 16 – 8 – 4 = 4 >0 …. Satisfies equation 3
When y = 5, y^2 – 2y – 4 = 25 – 10 – 4 = 11 >0 …. Satisfies equation 3
When y = 6, y^2 – 2y – 4 = 36 – 12 – 4 = 20 >0 …. Satisfies equation 3
When y = 7, y^2 – 2y – 4 = 49 – 14 – 4 = 31 >0 …. Satisfies equation 3

When y = 4, x = 6
When y = 5, x = 7
When y = 6, x = 8
When y = 7, x = 9

So the possible numbers are 64, 75, 86 and 97.

1) It is because when x increased by10%= x(1+10%)
and then decreased by 10%=1.1x(1-10%)
so the ans. should be 0.99x...not x
2)a.42
b.33