Quantitative Ability Test

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Quantitative Ability Test - 5

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Weekly Quiz Competition

Question 1
4 / -1

At what percentage above the cost price must an article be marked so as to gain 33% after allowing a discount of 5%?

A
38%

B
40%

C
43%

D
48%

Solution

\(\mathrm{MP}=\mathrm{CP} \frac{(100+\mathrm{Pr} \text { oft percentage })}{(100-\text { Discount percenatge })}\)
\(\mathrm{MP}=\mathrm{CP} \approx \frac{133}{95}=1.4 \mathrm{CP}\)
\(\therefore 40 \%\) above the \(\mathrm{CP}\)
Question 2
4 / -1

The average of 5 numbers is 65. The average of the first two numbers is 81 and the average of the last two numbers is 38. What is the third number?

A
63

B
87

C
99

D
Cannot be determined

Solution

The third number = 5 x 65 - 2 x 81 - 2 x 38

= 325 - 162 - 76 = 87
Question 3
4 / -1

A stream runs at 1 km/hr. A boat goes 35 km upstream and comes back again in 12 hr. The speed of the boat in still water is

A
6 km/hr

B
4.5 km/hr

C
3 km/hr

D
7.5 km/hr

Solution

Let the speed of boat in still water be \(x\) km \(12=\frac{35}{x-1}+\frac{35}{x+1}\)
\(-35\left[\frac{1}{x-1}+\frac{1}{x+1}\right]=35\left[\frac{2 x}{x^{2}-1}\right]\)
\(12 x^{2}-70 x-12=0\)
\(x=\frac{70 \pm \sqrt{4000+576}}{24}=\frac{70 \pm \sqrt{5476}}{24}=\frac{70+74}{24}\)
\(x=\frac{144}{24}=6 \quad \mathrm{km} / \mathrm{hr}\)
Question 4
4 / -1

Sum of four distinct two-digit prime numbers is 348. What is the difference between the largest and smallest of these prime numbers?

Enter your response (as an integer) using the virtual keyboard in the box provided below.

A
18

B
16

C
14

D
20

Solution

The sum of four numbers is 348. Therefore average = 348 / 4 = 87. Therefore at least one number out of the four is greater than 87. The only two digit prime numbers greater than 87 are 89 and 97.

The average of the four numbers would be 87 if sum of differences of numbers greater than the average from the average from the average.

If only one of 89 or 97 is the number greater than the average (87), the difference of that number from average would be either 2 or 10. All two digit prime numbers are odd therefore their differences from 87 are even numbers. No three distinct even numbers add up to 2 or 10. Therefore only one of 89 or 97 cannot be the number greater than 87. Therefore both 89 and 97 must be present in the remaining two numbers must be 162. Only two prime numbers that are less than 87 but add up to 162 are 83 and 79.

Therefore the four numbers are 79, 83, 89 and 97 and the difference between the smallest and largest among them is 18.
Question 5
4 / -1

The average age of 24 students and the principal is 15 years. When the principal's age is excluded, the average age decreases by 1 year. What is the age of the principal?

A
38years

B
40years

C
39years

D
Data inadequate

Solution

Average age of 24 students and the principal \(=15\) years. Total age of 24 students and the principal \(=15 \times 25=375\) years.
New average age of 24 students \(=15-1=14\) years Total age of 24 students \(=14 \times 24=336\) years
\(\therefore\) Age of the principal \(=375-336=39\) years.
Question 6
4 / -1

Ram started from Mumbai at x hrs y minutes and travelled to Pune. He reached Pune at y hrs z minutes. If the total travel time was z hrs and x minutes, his starting time in Mumbai could have been

A
02:08 hrs

B
13:03 hrs

C
00:02 hrs

D
12:01 hrs

Solution

x, y or z cannot be greater than 24

Also x + y + z cannot be greater than 24

Given x hrs + z hrs = y hrs

Also y min + x min = z min

The only value of x that will satisfy the above 2 equations is 0.

Hence, from among the choices given, the time could be 00:02 hrs
Question 7
4 / -1

The average age of 11 cricket players is increased by 3 years when two of the cricket players whose age is 21 years and 24 years is replaced by two new players. Find the average age of the two new players.

A
78years

B
48years

C
56years

D
39years

Solution

Total age increased = (11 x 3) = 33 years

Sum of ages of two new men = (33 + 21 + 24) years = 78 years

Average age of two new men = (78 / 2)=39 years
Question 8
4 / -1

A trader buys 78 kg of wheat for Rs. 492. He sells 40% of this at a loss of 20%. What should be the percentage mark up on the remaining so as to gain an overall 25%?

A
55%

B
60%

C
28%

D
45%

Solution

CP per kilogram \(=\frac{4 y 2}{78}=\operatorname{Rs} .6 .30\)
For an overall gain of \(25 \%\), the \(\mathrm{SP}\) of \(78 \mathrm{kg}\)
\(=492 \times \frac{1.25}{100}=\mathrm{Rs} .615\)
By selling \(40 \%\), i.e. \(31.2 \mathrm{kg}\) at a loss of \(20 \%\)
\(\mathrm{SP}_{+}=31.2 \times\left(\frac{492}{78}\right) \times \frac{80}{100}=\mathrm{Rs} .157 .44\)
Now the remaining ie. \((78-31.2)=46.8 \mathrm{kg}\) wheat to be sold for \((615-157.44)\) ie. Rs. 457.56
\(\mathrm{SP}_{2}=\frac{457.56}{46.8}=\mathrm{Rs} .9 .77\) per kilogram
Mark-up \(=\frac{9.77-6.3}{6.3}=55 \%\)
Question 9
4 / -1

3 unbaised coins are tossed. Final the probability of getting atleast 2 heads.

A
1/3

B
1/2

C
2/8

D
3/8

Solution

Total manber of possible events \(=2 \times 2 \times 2=8\) Favourable events \(=\) at least two heads \(+\) Al heads
. Requred probability \(=\frac{^{3} \mathrm{C}_{2}}{8}+\frac{^{2} \mathrm{C}_{2}}{8}\)
\(=\frac{3}{8}+\frac{1}{8}=\frac{4}{8}=\frac{1}{2}\)
Question 10
4 / -1

Bala had some 5-rupee and some 10-rupee coins. He had a total of 5 coins. Find the maximum possible value of all the coins with him (in Rs.).

A
60

B
55

C
50

D
45

Solution

Bala would have the maximum possible amount if he has the maximum number of 10- rupee coins. He must have at least one 5-rupee coin.

∴ He must have at most four 10-rupee coins.

∴ He would have the maximum possible amount when he has four 10-rupee coins.

This value (in Rs.) = (4) (10) + (1) (5) = 45.

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Re-Attempt Weekly Quiz Competition

Quantitative Ability Test - 5

Result

Quantitative Ability Test - 5

Score

-

Rank

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SHARING IS CARING

Question 1

38%

40%

43%

48%

Solution

Question 2

63

87

99

Cannot be determined

Solution

Question 3

6 km/hr

4.5 km/hr

3 km/hr

7.5 km/hr

Solution

Question 4

18

16

14

20

Solution

Question 5

38years

40years

39years

Data inadequate

Solution

Question 6

02:08 hrs

13:03 hrs

00:02 hrs

12:01 hrs

Solution

Question 7

78years

48years

56years

39years

Solution

Question 8

55%

60%

28%

45%

Solution

Question 9

1/3

1/2

2/8

3/8

Solution

Question 10

60

55

50

45

Solution

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