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Q:

The sum of the squares of two numbers is 3341 and the diference of their squares is 891. The numbers are :

A) 35 and 46	B) 35 and 50
C) 40 and 55	D) 45 and 60

Answer & Explanation Answer: A) 35 and 46

Explanation:

Let the numbers be x and y. Then,

x^2+y^2=3341......(1)

x^2-y^2=891......(2)

Adding (i) and (ii), we get : 2x^2=4232 or x^2= 2116 or x =46

Subtracting (ii) from (i), we get : 2y^2= 2450 or y^2 = 1225 or y = 35

So, the numbers are 35 and 46

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Q:

Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is :

A) 12	B) 137
C) 14	D) 15

Answer & Explanation Answer: D) 15

Explanation:

Let the three integers be x, x + 2 and x + 4. Then, 3x = 2 (x + 4) + 3 <=> x = 11.

Third integer = x + 4 = 15.

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Q:

If the sum and diference of two numbers are 20 and 8 respectively, then the difference of their squares is :

A) 120	B) 140
C) 160	D) 180

Answer & Explanation Answer: C) 160

Explanation:

Let the numbers be x and y. Then, x + y = 20 and x - y = 8.

x^2 - y^2 = (x + y) (x - y) = 20 x 8 = 160.

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Q:

A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is :

A) 253	B) 263
C) 273	D) 283

Answer & Explanation Answer: A) 253

Explanation:

Let the middle digit be x.

Then, 2x = 10 or x = 5. So, the number is either 253 or 352

Since the number increases on reversing the digits, so the hundred's digit is smaller than the unit's digit.

Hence, required number = 253.

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Q:

In a two-digit number, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is :

A) 12	B) 24
C) 36	D) 48

Answer & Explanation Answer: B) 24

Explanation:

Let the ten's digit be x.

Then, unit's digit = x + 2.

Number = 10x + (x + 2) = 11x + 2

Sum of digits = x + (x + 2) = 2x + 2.

(11x + 2) (2x + 2) = 144

=> 22x^2+26x-140=0

=> (x - 2)(11x + 35) = 0

=> x = 2

Hence, Required Number = 11x + 2 = 24

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Q:

The denominator of a fraction is 3 more than the numerator. If the numerator as well as the denominator is increased by 4, the fraction becomes 4/5. What was the original fraction ?

A) 7/11	B) 8/11
C) 9/11	D) 10/11

Answer & Explanation Answer: B) 8/11

Explanation:

Let the numerator be x Then, denominator = x + 3.

Now. (x + 4)/(x + 3) +4 = 4/5 <=> 5 (x + 4) = 4(x + 7)

=> x = 8.

The fraction is 8/11.

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Q:

The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is :

A) 100	B) 200
C) 300	D) 400

Answer & Explanation Answer: D) 400

Explanation:

Let the numbers be x and y.

Then, xy = 9375 and x/y = 15.

$(\frac{x y}{\frac{x}{y}}) = 9375 / 15$

=> $y^{2} = 625$

=> y = 25

=> x = 15y = 15 x 25 = 375.

Sum of the numbers = 375 + 25 = 400.

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Q:

The sum of the digits of a two-digit number is 9 less than the number. Which of the following digits is at unit's place of the number ?

A) 1	B) 2
C) 3	D) data inadequate

Answer & Explanation Answer: D) data inadequate

Explanation:

Let the ten's digit be x and unit's digit be y. Then, (10x + y) - (x + y) = 9 or x = 1.

From this data we cannot find y, the unit's digit. So the data is inadequate..

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