Quantitative Aptitude Test

Result

Quantitative Aptitude Test - 9

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Weekly Quiz Competition

Question 1
4 / -1

In a triangle PQR, if ∠P = 60° , Find ∠QIR, where I is the incentre of the triangle.

A
115°

B
120°

C
90°

D
130°

Solution

By Property of triangles, Central angle is twice that of the inscribed angle. If you join QI, then the angle subtended by the chord at I which is ∠QIR will be twice that of the angle subtended by the chord at a point on the circle. Now ∠P = 60°

∴ ∠QIR = 120°
Question 2
4 / -1

If x and y are positive real numbers such that x + y = 10, then what is the maximum value of x²y²

A
16

B
256

C
625

D
15696

Solution

If the sum of two terms is constant, then the product of those terms will be maximum when the quantities are equal

∴ x + y + x + y = 20

x = y = 20/4 = 5
Question 3
4 / -1

For the two real numbers a and b, which of the following is true?

A
ab is always positive

B
a+b is always positive

C
a-b is always positive

D
None of these

Solution

Nothing is mentioned about the sign of a and b

So we cannot comment about their product, sum, or difference.

Hence mark d
Question 4
4 / -1

5Kg of sugar costing Rs.20/Kg is added to 10Kg of sugar costing Rs.35/kg. At what price (in Rs.) should this mixture be sold so that there is no loss or gain?

A
15

B
35

C
30

D
25

Solution

5Kg of sugar costing Rs.20/Kg, Cost price becomes = 5Kg x Rs.20/Kg = Rs.100

10Kg of sugar costing Rs.35/Kg, Cost price becomes = 10Kg x Rs.35/Kg = Rs.350

Selling price of the mixture should be Rs.100 + Rs.350 (So that there is no loss or gain) =Rs.450

Hence mark option c
Question 5
4 / -1

Each of the questions below consists of a question and 2 statements numbered I and II given below it. Give answer

What is the percent profit/loss made/incurred by selling an article for Rs 24000?

I. The ratio between the selling price and the cost price of the article is 5 : 3 respectively

II. The difference between cost and selling price is Rs 9000

A
If data in only one of the two statements is sufficient to answer.

B
If data in either statement I or II alone is sufficient to answer.

C
If data in neither statement I nor II is sufficient to answer.

D
If data in both the statements I and II are necessary to answer the question.

Solution

If SP = 24000 which is the 5/8th part as per the ratio given

Thus CP is the 3/8th part, thus Rs. 9000

Clearly we need to calculate profit percentage now,

Thus Profit = 24000 – 9000 = 15000

Thus % profit = 15000/9000 * 100 = 5/3*100 = 166.66%

Second statement does not specify profit or loss

Hence, the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question
Question 6
4 / -1

Each of the questions below consists of a question and 2 statements numbered I and II given below it.

What is the speed of the boat in still water?

I. The boat travels at the speed of 4km/hr upstream.

II. The boat travels at 6 km/per hr downstream.

A
If data in only one of the two statements is sufficient to answer.

B
If data in either statement I or II alone is sufficient to answer.

C
If data in neither statement I nor II is sufficient to answer.

D
If data in both the statements I and II are necessary to answer the question.

Solution

the data in both the statements I and II together is necessary to answer the question

Let the speed of the Boat be ‘x’. Let the speed of the water current be ‘y’

1st Statement : Upstream = x – y = 4

2nd Statement : Downstream = x + y = 6

On Solving simultaneous eq. we get x= 5, Y = 1
Question 7
4 / -1

Study the following graph carefully to answer the questions that follow.

What is the respective ratio between the numbers of students passed from University ‘A’ in year 2007 and the number of students passed from University B in the year 2004?

A
5:4

B
4:5

C
7:10

D
10:7

Solution

Hence mark option d
Question 8
4 / -1

Study the following graph carefully to answer the questions that follow:

If for a certain quantity of books, the publisher has to pay Rs. 1360 as printing cost, then what will be amount of royalty to be paid for these books?

A
Rs. 1000.2

B
Rs. 1002

C
Rs. 1020

D
Rs. 1200

Solution

Let the amount of Royalty to be paid for these books be Rs. r.
Question 9
4 / -1

A man engaged a servant on the condition that he would pay him Rs. 90 and also give him a gift voucher after service of one year. He served only for nine months and received gift voucher and Rs. 65. Find the value of the gift voucher in rupees.

A
10

B
9

C
0

D
2.5

Solution

Let x be the value of the voucher. The man was supposed get paid Rs. 90+x if he had completed the one year. Instead he completed only three quarters of the period.

Therefore,

solving which we get the value of x (gift voucher) as 10.
Question 10
4 / -1

The digits of a two digit number differ by eight. Find the difference between the number and the number formed by reversing its digits.

A
54

B
72

C
81

D
63

Solution

Given:

Two digits number differ by 8

To find:

The difference of the number and the number formed after reversing

Solution:-

Let the two digits number be x and y

Difference between two digits=8

So,(x-y)=6

Now, Let the tens digits be 10x and unit digit be y (10x+y)

After reversing it will be (10y+x)

Now,According to the question

=(10x+y)-(10y+x)

=10x+y-10y-x

=9x-9y

=9(x-y)

Taking (x-y)=8. {Given above}

=9(8)

=9×8

=72