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SSC CGL Tier1 Quantitative Aptitude Average Test 3

1640.In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
6.25
6.5
6.75
7
Explanation:
Required run rate =$ \left(\dfrac{282 - (3.2 \times 10)}{40} \right) $=$ \dfrac{250}{40} $   = 6.25
1641.The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
0
1
10
19
Explanation:

Average of 20 numbers = 0.

$\therefore$ Sum of 20 numbers $\left(0 \times 20\right)$ = 0.

It is quite possible that 19 of these numbers may be positive and if their sum is $ a $ then 20th number is $\left(- a \right)$.

1642.The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. Find out the average age of the team.
23 years
20 years
24 years
21 years
Explanation:

Number of members in the team = 11

Let the average age of of the team = $x$

=> $\dfrac{\text{Sum of ages of all 11 members}}{11} = x$

=> Sum of the ages of all 11 members = $11x$

Age of the captain = 26

Age of the wicket keeper = 26 + 3 = 29

Sum of the ages of 9 members of the team excluding captain and wicket keeper

$= 11$x$ - 26 - 29 = 11$x$ - 55$

Average age of 9 members of the team excluding captain and wicket keeper

$=\dfrac{11x - 55 }{9}$

Given that $\dfrac{11x - 55 }{9} = \left(x - 1\right)$

$\Rightarrow 11x - 55 = 9 \left(x - 1\right)$

$\Rightarrow 11x - 55 = 9x - 9$

$\Rightarrow 2x = 46$

$\Rightarrow x = \dfrac{46}{2} = 23\text{ years}$

1643.The average score of a cricketer for ten matches is 38.9 runs. If the average for the first six matches is 42, what is the average for the last four matches?
34.25
36.4
40.2
32.25
Explanation:

Total runs scored in 10 matches = $10 \times 38.9$

Total runs scored in first 6 matches =$ 6 \times 42$

Total runs scored in the last 4 matches =$ 10 \times 38.9 - 6 \times 42$

Average of the runs scored in the last 4 matches = $\dfrac{10 \times 38.9 - 6 \times 42}{4}$

$=\dfrac{389 - 252}{4}$

$=\dfrac{137}{4}$

$= 34.25$

1644.A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?
28 $ \dfrac{4}{7} $years
31 $ \dfrac{5}{7} $years
32 $ \dfrac{1}{7} $years
None of these
Explanation:
Required average =$ \left(\dfrac{67 \times 2 + 35 \times 2 + 6 \times 3}{2 + 2 + 3} \right) $
=$ \left(\dfrac{134 + 70 + 18}{7} \right) $
=$ \dfrac{222}{7} $
= 31 $ \dfrac{5}{7} $years.
1652.If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is:
53.33
54.68
55
None of these
Explanation:
Required average =$ \left(\dfrac{55 \times 50 + 60 \times 55 + 45 \times 60}{55 + 60 + 45} \right) $
=$ \left(\dfrac{2750 + 3300 + 2700}{160} \right) $
=$ \dfrac{8750}{160} $
= 54.68
1653.The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
23 years
24 years
25 years
None of these
Explanation:

Let the average age of the whole team by $ x $ years.

$\therefore 11 x - (26 + 29) = 9\left( x -1 \right)$

$\Rightarrow$ 11$ x $ - 9$ x $ = 46

$\Rightarrow$ 2$ x $ = 46

$\Rightarrow x $ = 23.

So, average age of the team is 23 years.

1654.A student needed to find the arithmetic mean of the numbers 3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14 and x. He found the mean to be 12. What is the value of x?
12
5
7
9
Explanation:

$\dfrac{\text{3+11+7+9+15+13+8+19+17+21+14+}x}{12}$ $ = 12$

$\Rightarrow \dfrac{137 + x}{12} = 12\\~\\$

$\Rightarrow 137 + x = 144\\~\\$

$\Rightarrow x = 144 - 137 = 7$

1658.The batting average for 40 innings of a cricket player is 50 runs. His highest score exceeds his lowest score by 172 runs. If these two innings are excluded, the average of the remaining 38 innings is 48 runs. Find out the highest score of the player.
150
174
180
166
Explanation:

Total runs scored by the player in 40 innings = $ 40 \times 50$

Total runs scored by the player in 38 innings after excluding two innings = $ 38 \times 48$

Sum of the scores of the excluded innings = $ 40 \times 50 - 38 \times 48 = 2000 - 1824 = 176$

Given that the scores of the excluded innings differ by 172. Hence lets take

the highest score as x + 172 and lowest score as $x$

Now $x + 172 + x$ = 176

=> 2$x$ = 4

=> $x=\dfrac{4}{2}$ = 2

Highest score = $x$ + 172 = 2 + 172 = 174

1660.In Aruns opinion, his weight is greater than 65 kg but less than 72 kg. His brother doest not agree with Arun and he thinks that Aruns weight is greater than 60 kg but less than 70 kg. His mothers view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Arun?
67 kg.
68 kg.
69 kg.
Data inadequate
Explanation:

Let Aruns weight by X kg.

According to Arun, 65 < X < 72

According to Aruns brother, 60 < X < 70.

According to Aruns mother, X <= 68

The values satisfying all the above conditions are 66, 67 and 68.

$\therefore$ Required average =$ \left(\dfrac{66 + 67 + 68}{3} \right) $=$ \left(\dfrac{201}{3} \right) $= 67 kg.
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