# Aptitude Decimal Fraction Test Paper 3

11) Let x = 0.841̅8̅1. when x is written as a fraction in lowest terms, the denominator exceeds the numerator by

1. 12
2. 14
3. 21
4. 87

Explanation:

We can write f = 0.841̅8̅1 in fraction form = (84181-841)/ 99000 = 83340/ 99000
Or, 463/ 550
Therefore, denominator - numerator = 550 - 463 = 87

12) The expression [24.23 * 1.423 * 34.21]/ [521.3 * 413.32 * 2.53] is the same as

1. [2423*1423*3421]/ [5213 * 41332 * 253]
2. [242.3*142.3*3421]/ [5213*4133.2*2.53]
3. [2.423*14.23*342.1]/ [521.3*4133.2*2.53]
4. None of these

Explanation:

The value of actual expression [24.23 * 1.423 * 34.21]/ [521.3 * 413.32 * 2.53] = 0.002163
Now, According to option a [2423*1423*3421]/ [5213*41332*253] = 0.2163
Now, According to option b [242.3*142.3*3421]/ [5213*4133.2*2.53] = 2.1637
Now, according to option c [2.423*14.23*342.1]/ [521.3*4133.2*2.53] = 0.002163
The option C gives the same value as the actual expression, so it is the correct answer.

Solution 2:

The original expression [24.23 * 1.423 * 34.21]/ [521.3 * 413.32 * 2.53] can be written as
[2423*1423*3421*10*100*100]/ [5213*41332*253*100*1000*100]
Or, [2423*1423*3421*105]/ [5213*41332*253*107]
Or, [2423*1423*3421]/[5213*41332*253*102].......... (i)
Now, according to option a [2423*1423*3421]/ [5213*41332*253]......... (ii)
Now, according to option b [2423*1423*3421*103]/ [5213*41332*253*102]
Or, [2423*1423*3421*10]/ [5213*41332*253]........ (iii)
Now, according to option c [2423*1423*3421*104]/ [5213*41332*253*106]
Or, [2423*1423*3421]/ [5213*41332*253*102].......... (iv)

Since, equation i and iv have the same power of 10 in the denominator.

Hence, we can say option C is the same as the actual expression.

13) Find the approximate value of x from the given expression:
29.38*37.05/x + 7.45 = 100.5

1. 10
2. 14.5
3. 13
4. 12

Explanation:

ATQ, 29.38 * 37.50/x +7.45 = 100.5
Now, according to BODMAS rule
29.38* 37.50/ x = 100.5- 7.45
Or, 29.38 * 37.50 = 93.05 * x
Or, x = (29.38*37.50)/ 93.05
Hence, x = 11.6983, or the approximate value = 12.

14) The value of [(0.01)2 + (0.22)2 + (0.333)2]/ [(0.001)2 + (0.022)2 + (0.0333)2] is

1. 1/10
2. 10
3. 100
4. 1000

Explanation:

We can write the expression as [(0.01) 2 + (0.22) 2 + (0.333) 2]/ [(0.01/10) 2 + (0.22/10) 2 + (0.333/10) 2]
Or, [(0.01) 2 + (0.22) 2 + (0.333) 2] / [(0.01) 2 + (0.22) 2 + (0.333) 2] * (1/100)
Or, [(0.01) 2 + (0.22) 2 + (0.333) 2] * 100/ [(0.01) 2 + (0.22) 2 + (0.333) 2]

Hence, numerator and denominator will cancel each other, and the remaining value will be 100.

15) The value of (3.87 - 2.59) equals to

1. 1.20
2. 1.2
3. 1.27
4. 1.28

Explanation:

3.87 = 3+ (87/ 99) = 3+ (29/33) = 128/33............ (i)
And, 2.59 = 2+ (59/99) = 257/ 99............. (ii)

From equation (i) and (ii):

(128/33) - (257/99)
LCM of 33 and 99 is 99
So, (3* 128 - 257)/ 99 = 1.282828...
Hence, we can write it as 1.28

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Decimal Fraction Concepts   