Mathematics for Competitive exam

Decimal Fraction

1. Evaluate 3.82−1.223.8−1.2
A. 5.2	B. 4.8
C. 4	D. 5

2. If 204 ÷ 12.75 = 16, then 2.04 ÷ 1.275 = ?
A. 16	B. 1.6
C. 0.16	D. 0.016

3. 0.03 × 0.0124 = ?
A. 3.72 × 10-6	B. 3.72 × 10-5
C. 3.72 × 10-3	D. 3.72 × 10-4

4. 7212 + 15.231 - ? = 6879
A. 359.022	B. 362.02
C. 328.221	D. 348.231

5. 4211.01 + 22.261 - ? = 2645.759
A. 1587.512	B. 1586.532
C. 1588.021	D. 1586.422

6. The price of commodity P increases by 40 paise every year, while the price of commodity Q increases by 15 paise every year. If in 2001, the price of commodity P was Rs. 4.20 and that of Q was Rs. 6.30, in which year commodity P will cost 40 paise more than the commodity Q ?
A. 2008	B. 2009
C. 2010	D. 2011

7. Which of the following fractions is greater than 3/5 and less than 6/7?
A. 78	B. 13
C. 23	D. 12

8. 0.004 × 0.5 = ?
A. None of these	B. 0.02
C. 0.002	D. 0.0002

9. How many digits will be there to the right of the decimal point in the product of 89.635 and .02218?
A. 5	B. 6
C. 7	D. 8

10. 4.86¯¯¯¯−3.71¯¯¯¯ = ?
A. 1.6¯	B. 1.5¯
C. 1.14¯¯¯¯	D. 1.15¯¯¯¯

Answer With Explanation

1.Answer : Option D

Explanation :

a2−b2=(a−b)(a+b)

3.82−1.223.8−1.2=(3.8+1.2)(3.8−1.2)(3.8−1.2)=3.8+1.2=5

2.Answer : Option B

20412.75=16⇒20.41.275=16(∵ Divided Numerator and Denominator by 10))⇒2.041.275=1.6(∵ Divided LHS and RHS by 10)

3.Answer : Option D

Explanation :

3 × 124 = 372

Sum of the decimal places in 0.03 and 0.0124 = 2 + 4 = 6

Hence, 0.03 × 0.0124 = 372 × 10^-6 = 3.72 × 10^-4

4. Answer : Option D

Explanation :

Required Value = 7212 + 15.231 - 6879 = 348.231

5.Answer : Option A

Explanation :

Required Value = 4211.01 + 22.261 - 2645.759 = 1587.512

6. Answer : Option D

Explanation :

Let the commodity P costs 40 paise more than the commodity Q after n years

Price of the commodity P in 2001 = Rs.4.20

Since the price of the commodity P increases by Rs 0.40 every year,
Price of the commodity P after n years from 2001 = Rs.4.20 + (n × .40)

Price of the commodity Q in 2001 = Rs.6.30

Since the price of the commodity Q increases by Rs 0.15 every year,
price of the commodity Q after n years from 2001 = Rs.6.30 + (n × .15)

Since the commodity P costs Rs. 0.40 more that the commodity Q after n years from 2001,
4.20 + (n × .40) = 6.30 + (n × .15) + 0.40

=> (40n - .15n) = 6.30 - 4.20 + 0.40 = 2.5

=> .25n = 2.5

⇒n=2.5.25=25025=10

=> Commodity P costs Rs.0.40 more that the commodity Q after 10 years from 2001

7. Answer : Option C

Explanation :

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Solution 1
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35=0.667=0.85(Taken only the first two digits after the decimal point)
Hence, the question is to find out a number which is greater than 0.6 and less than 0.85

The given choices are



12=0.523=0.66(Taken only the first two digits after the decimal point)13=0.33(Taken only the first two digits after the decimal point)78=0.87(Taken only the first two digits after the decimal point)


Clearly, 0.66 = 23 is the answer
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Solution 2
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LCM of 5, 7, 2, 3, 3, 8  = 840



35=50484067=720840
Hence, the question is to find out a number which is between the above numbers

The given choices are



12=42084023=56084013=28084078=735840


Clearly, 560840=23 is the answer

8. Answer : Option C

Explanation :

0.004 × 0.5 = 0.002

9. Answer : Option C

Explanation :

Sum of decimal places = 3 + 5 = 8

The last digit to the extreme right is zero (Since 5 x 8 = 40)

Hence, there will be 7 significant digits to the right of the decimal point.

10. Answer : Option D

Explanation :

4.86¯¯¯¯=(4+8699)

3.71¯¯¯¯=(3+7199)

Hence, 4.86¯¯¯¯−3.71¯¯¯¯=(4+8699)−(3+7199)=(1+1599)=1.15¯¯¯¯

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