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__Numbers and Ages Questions - Numbers and Ages Quiz Details__

__Numbers and Ages Formulae__

Numbers

1. (a + b)(a - b) = (a2 - b2)

2. (a + b)2 = (a2 + b2 + 2ab)

3. (a - b)2 = (a2 + b2 - 2ab)

4. (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)

5. (a3 + b3) = (a + b)(a2 - ab + b2)

6. (a3 - b3) = (a - b)(a2 + ab + b2)

7. (a3 + b3 + c3 - 3abc) = (a + b + c)(a2 + b2 + c2 - ab - bc - ac)

8. When a + b + c = 0, then a3 + b3 + c3 = 3abc.

Ages

1. Age after n years = X + n

2. Age n years ago = X “ n

3. n times the age = nX

4. Age of y = (Ratio of y/Sum of ratios)Ã— sum of ages

5. Age of y = (q/p+q)Ã— A

Online Test Name |
Numbers and Ages |

Exam Type |
Multiple Choice Questions |

Category |
Aptitude Quiz |

Number of Questions |
53 |

1. (a + b)(a - b) = (a2 - b2)

2. (a + b)2 = (a2 + b2 + 2ab)

3. (a - b)2 = (a2 + b2 - 2ab)

4. (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)

5. (a3 + b3) = (a + b)(a2 - ab + b2)

6. (a3 - b3) = (a - b)(a2 + ab + b2)

7. (a3 + b3 + c3 - 3abc) = (a + b + c)(a2 + b2 + c2 - ab - bc - ac)

8. When a + b + c = 0, then a3 + b3 + c3 = 3abc.

Ages

1. Age after n years = X + n

2. Age n years ago = X “ n

3. n times the age = nX

4. Age of y = (Ratio of y/Sum of ratios)Ã— sum of ages

5. Age of y = (q/p+q)Ã— A

1. The sum of three consecutive integers is 102. Find the lowest of the three?
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Answer: Option D

Explanation:

Three consecutive numbers can be taken as (P - 1), P, (P + 1).

So, (P - 1) + P + (P + 1) = 102

3P = 102 => P = 34.

The lowest of the three = (P - 1) = 34 - 1 = 33.

2. The sum of the two digits of a number is 10. If the number is subtracted from the number obtained by reversing its digits, the result is 54. Find the number?
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Answer: Option B

Explanation:

Any two digit number can be written as (10P + Q), where P is the digit in the tens place and Q is the digit in the units place.

P + Q = 10 ----- (1)

(10Q + P) - (10P + Q) = 54

9(Q - P) = 54

(Q - P) = 6 ----- (2)

Solve (1) and (2) P = 2 and Q = 8

The required number is = 28

3. The sum of three consecutive even numbers is 42. Find the middle number of the three?
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Answer: Option A

Explanation:

Three consecutive even numbers (2P - 2), 2P, (2P + 2).

(2P - 2) + 2P + (2P + 2) = 42

6P = 42 => P = 7.

The middle number is: 2P = 14.

4. The numerator of a certain fraction is 8 less than the denominator. If 3 is added to the numerator and 3 is subtracted from the denominator, the fraction becomes 3/4. Find the original fraction?
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Answer: Option C

Explanation:

The denominator be P, the numerator will be (P - 8).

The fraction will be (P - 8)/P.

Adding 3 to the numerator and subtracting 3 from the denominator, (P - 8 + 3)/(P - 3) = 3/4.

(P - 5)/(P - 3) = 3/4

P = 20 - 9 => P = 11.

The fraction is: 3/11.

5. The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 5 years hence?
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Answer: Option C

Explanation:

A + B = 60, A = 2B

2B + B = 60 => B = 20 then A = 40.

5 years, their ages will be 45 and 25.

Sum of their ages = 45 + 25 = 70.