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Q:

The minimum number of half years in which a sum of money kept at 60% compound interest will be quadrupled is ?

A) 2	B) 4
C) 3	D) 6

Answer & Explanation Answer: D) 6

Explanation:

Let us assume Amount be 100 Rs and we calculate in CI

First year 60% of 100 = 60 amount (100+60) is 160

Second year 60% of 160 = 96 amount (160+96) is 256

Third year 60% of 256 =153.6 amount (256+153.6) is 409.6

Here the Amount of 100 Rs is quadrapled in 3 years.

One year contains 2 half years

Three year has 6 half years.

Therefore, It takes 6 half years.

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Filed Under: Compound Interest
Exam Prep: CAT
Job Role: Bank PO

Q:

If the cost price of a certain object doubles, then the loss gets tripled of what it was initially. The initial loss % was ?

A) 0 %	B) 25 %
C) 75 %	D) 50 %

Answer & Explanation Answer: D) 50 %

Explanation:

Let the cost price be x and selling price be y.
Loss = x – y

When the cost price doubles, the loss gets tripled.
So it becomes like this, 2x – y = 3(x-y)

=> x = 2y

Loss % = (loss/ C.P) x 100 = [(2y-y)/2y] x 100= 50 %

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Filed Under: Profit and Loss
Exam Prep: CAT
Job Role: Bank PO

Q:

A man is riding a bike with front and back wheel circumference of 40 inches and 70 inches respectively. If the man rides the bike on a straight road without slippage, how many inches will the man have travelled when the front wheel has made 15 revolutions more than the back wheel?

A) 1100	B) 1300
C) 1400	D) 1200

Answer & Explanation Answer: C) 1400

Explanation:

Given the ratio of the circumference of front wheel is 40 inches and back wheel is 70 inches.

Distance covered = Circumference of the wheel × No. of Revolutions made by the wheel

If n is the number of revolutions made by back wheel, the number of revolutions made by front wheel is n+15

Distance covered by both the wheels is the same

i.e, 40*(n+15)=70n

n=20

Front wheel : Back Wheel

Circumference 40 : 70

Revolutions 35 : 20

Distance covered : 40×35 = 70×20 = 1400 inches.

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Filed Under: Time and Distance
Exam Prep: CAT
Job Role: Bank PO

Q:

Some mangoes are yellow.
Some tixo are mangoes.

Conclusions:
(i) Some mangoes are green.
(ii) Tixo is a yellow.

A) Only conclusion (i) follows	B) Only conclusion (ii) follows
C) Either (i) or (ii) follows	D) Neither (i) nor (ii) follows

Answer & Explanation Answer: D) Neither (i) nor (ii) follows

Explanation:

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Filed Under: Verification of Truth of the statement
Exam Prep: CAT
Job Role: Bank Clerk

Q:

Determine which of the given conclusions logically follows from the given statements, disregarding commonly known facts.

Statements:
Some actors are singers.
All the singers are dancers.

Conclusions:
(i) Some actors are dancers.
(ii) No singer is an actor.

A) Neither (i) nor (ii) follows	B) Either (i) or (ii) follows
C) Only conclusion (ii) follows	D) Only conclusion (i) follows

Answer & Explanation Answer: D) Only conclusion (i) follows

Explanation:

Some + All = Some

and the common word in two statements is Singers will not be used.

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Filed Under: Verification of Truth of the statement
Exam Prep: CAT
Job Role: Bank PO

Q:

How many prime numbers exist in $6^{5} \times 35^{9} \times 11^{3}$ ?

A) 29	B) 31
C) 33	D) 27

Answer & Explanation Answer: B) 31

Explanation:

Given $6^{5} \times 35^{9} \times 11^{3}$

$\Rightarrow {(2 \times 3)}^{5} \times {(5 \times 7)}^{9} \times 11^{3}$

$\Rightarrow 2^{5} \times 3^{5} \times 5^{9} \times 7^{9} \times 11^{3}$

Thus, there are (5 + 5 + 9 + 9 + 3)= 31 prime numbers.

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Filed Under: Numbers
Exam Prep: CAT
Job Role: Bank PO

Q:

How many numbers with distinct digits are possible product of whose digits is 18?

A) 12	B) 8
C) 6	D) 4

Answer & Explanation Answer: B) 8

Explanation:

Two digit numbers: The two digits can be 2 and 9: Two possibilities 29 and 92.

Three-digit numbers: The three digits can be 1, 2 and 9 => 3! Or 6 possibilities.

We cannot have three digits as (3, 3, 2) as the digits have to be distinct.

We cannot have numbers with 4 digits or more without repeating the digits.

So, there are totally 8 numbers.

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Filed Under: Numbers
Exam Prep: CAT
Job Role: Bank Clerk

Q:

5 sin(x)+ 12 cos(x) + r is always greater than or equal to zero. What is the smallest value satisfied by 'r' ?

A) -13	B) 11
C) 13	D) -11

Answer & Explanation Answer: C) 13

Explanation:

Given,

5sinx + 12cosx ≥ -r

$\Rightarrow 13 (\frac{5}{13} \sin x + \frac{12}{13} \cos x) \geq - r$ cosx) ≥ -r

$\frac{5}{13}$ = cosA => sinA = $\frac{12}{13}$

=> 13(sinx cosA + sinA cosx) ≥ -r

=> 13(sin(x + A)) ≥ -r

we know that , -1 ≤ sin (angle) ≤ 1

=> 13sin (x + A) ≥ -13 $\Rightarrow r_{m i n} = 13$

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Filed Under: Simplification
Exam Prep: CAT
Job Role: Bank PO

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