Quantitative Aptitude (QA) Test

Result

Quantitative Aptitude (QA) Test - 34

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Question 1
3 / -1

If a and b be two positive integers, then a² + b² + ab can be equal to

A
310

B
306

C
320

D
316

Solution
Question 2
3 / -1

In a triangle PQR, the length of altitude PS is 18cm, and this altitude divides QR such that QS:SR = 19:81. Find the length (in cm) of a line segment parallel to the altitude which bisects the area of the triangle PQR.

A

B

C

D

Solution
Question 3
3 / -1

For any natural numbers m, n, and k, such that k divides both m + 2n and 3m + 4n, k must be a common divisor of

A
2m and 3n

B
2m and n

C
m and n

D
m and 2n

Solution

Since k divides (m + 2n), k must also divides (2m + 4n)

Also, k divides (3m + 4n) => k divides (m + 2m + 4n)

So, k must divide m as well

Again k divides (m + 2n), k must also divides (3m + 6n)

Also, k divides (3m + 4n) => k divides (3m + 6n + 2n)

So, k must divide 2n as well

Hence, k must be a common divisor of m and 2n.
Question 4
3 / -1

Consider a circle with centre O as shown in the figure below. YZ is a tangent to the given circle. It is also given that XM = 8 units, MY = 6 units, ZY = 12 units, and OX = 2 units. Find the length of the radius of the circle.

A

B

C

D

Solution
Question 5
3 / -1

A well with 10m inside diameter is dug 14m deep. Earth taken out of it has been spread evenly around it, to a width of 5m. Find the height of the embankment so formed.

A

B

C

D

Solution
Question 6
3 / -1

If x = Log_abc + 1, y = Log_bac + 1 and z = Log_cab + 1 then find out the value of

A
Log(a + b + c)

B
0

C
Log_abc

D
1

Solution
Question 7
3 / -1

Find out the number of numbers between 4600 and 8700 (including both numbers) in which digits 3, 7 and 9 do not appear?

A
866

B
978

C
858

D
1078

Solution

The digit at thousand place is fixed here. We need to arrange hundred, tens and unit digit

Total such numbers = 98 + 343 + 343 + 294 = 1078.
Question 8
3 / -1

A sum of money becomes four times with certain rate of interest where interest being calculated on compounding basis in 2 years’ time. Find out the number of years would it take to become 8 times under simple interest with rate of interest is 75% of prior interest rate. (Write your answer in X/Y fraction format)

A

B

C

D

Solution
Question 9
3 / -1

There is a group of 12 people. Assuming there is no such concept of leap year, find out the probability of at least 2 people have the same birthday in a group

A

B

C

D

Solution

Without a leap year, there are 365 days in a year

Every person can have birthday at any given date

For every person possible cases are 365

Total possible outcomes = 365¹²(365×365×…..for each and every person of the group)

Now, at least two of them have same birthday

We will find out none of the person have same birthday and will subtract it from 1

No two person have same birthday = ³⁶⁵P₁₂

So, the required probability is
Question 10
3 / -1

If ‘x’ tomatoes out of 40 are sold at (x)% profit and the remaining at 1 - x%, then what will be the minimum profit that can be earned if each tomato costs Rs.3?

A
33.5

B
46.5

C
59.0

D
63.45

Solution