model 5 smallest and largest fraction/numbers Practice Questions Answers Test with Solutions & More Shortcuts

Question : 6 [SSC CHSL 2013]

If a number is as much greater than 31 as it is less than 75, then the number is

a) 74

b) 53

c) 44

d) 106

Answer: (b)

If the number be x, then

x – 31 = 75 – x

⇒ 2x = 75 + 31 = 106

⇒ x = 53

Question : 7 [SSC CAPFs & CISF 2013]

The greatest among the following numbers $(3)^{1/3}, (2)^{1/2}, 1, (6)^{1/6}$ is :

a) $(6)^{1/6}$

b) $(3)^{1/3}$

c) 1

d) $(2)^{1/2}$

Answer: (b)

LCM of 3, 2 and 6 = 6

∴ $(3)^{1/3}$ = $(3^2)^{1/6}$ = $(9)^{1/6}$

$(2)^{1/2}$ = $(2^3)^{1/6}$ = $(8)^{1/6}$

$(1)^{1/6}$ = 1; $(6)^{1/6}$ = $(6)^{1/6}$

Question : 8

Which of the following fraction is the smallest? $7/6, 7/9, 4/5, 5/7$

a) $4/5$

b) $5/7$

c) $7/ 9$

d) $7/6$

Answer: (b)

$7/6$ = 1.166 ; $7/9$ = 0.777; $4/5$ = 0.8 and $5/7$ = 0.714

Therefore, the smallest number is $5/7$

Question : 9 [SSC CGL Prelim 2003]

Which of the following is the largest fraction ? $6/7, 5/6, 7/8, 4/5$

a) $5/6$

b) $7/8$

c) $4/5$

d) $6/7$

Answer: (b)

The decimal equivalents of :

$6/7 = 0.857, 5/6 = 0.833$

$∴7/8 = 0.875, 4/5 = 0.8$

Obviously, 0.875 is the greatest.

$7/8$ is the largest fraction.

Question : 10 [SSC CGL Tier-II 2015]

Sum of three fractions is 2$11/24$ . On dividing the largest fraction by the smallest fraction, $7/6$ is obtained which is $1/3$ greater than the middle fraction. The smallest fraction is

a) 5/6

b) 3/7

c) 3/4

d) 5/8

Answer: (c)

Let the three fractions be p, q and r,

where p < q < r.

According to the question,

$r/p$ = $7/6$ ⇒ r = $7/6$ p

Again, middle fraction

= q = $7/6$ - $1/3$ = ${7-2}/6$ = $5/6$

∴ p+q+r = 2$11/24$

⇒ p + $5/6$ + $7/6$p = $59/24$

⇒ p+${7p}/6$ = $59/24$ - $5/6$

⇒ ${6p+7p}/6$ = ${59-20}/24$ = $93/24$

⇒ 13p = $39/24$×6 = $39/4$

⇒ p = $39/{4×13}$ = $3/4$

IMPORTANT quantitative aptitude EXERCISES

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