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Q:

The difference between a two-digit number and the number obtained by interchanging the two digits is 63. Which is the smaller of the two numbers ?

A) 12	B) 15
C) 17	D) none of these answers can be determined

Answer & Explanation Answer: D) none of these answers can be determined

Explanation:

Let the ten's digit be x and unit's digit be y.

Then, (10x + y) - (10y + x) = 63

=> 9 (x - y) = 63

=> x - y = 7.

Thus, none of the numbers can be deermined..

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Filed Under: Problems on Numbers

Q:

There are two numbers such that the sum of twice the first and thrice the second is 39, while the sum of thrice the first, and twice the second is 36. The larger of the two is :

A) 3	B) 6
C) 9	D) 12

Answer & Explanation Answer: C) 9

Explanation:

Let the numbers be x and y. Then, 2x + 3y = 39...(i)and 3x + 2y = 30 ...(ii)

On solving (i) and (ii), we get : x = 6 and y = 9.

larger number = 9

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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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Filed Under: Problems on Numbers

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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Filed Under: Problems on Numbers

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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Filed Under: Problems on Numbers

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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Filed Under: Problems on Numbers

Q:

The product of three consecutive even numbers when divided by 8 is 720. The product of their square roots is :

A) 12 sqrt(10)	B) 24 sqrt(10)
C) 120	D) none of these

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