CMAT 2018 Slot 1

Let the marked price of two balls be X

Given that they were bought at 37.40 rupees at 15% discount.

=> X x $$\ \frac{\ 85}{100}$$=37.40

X= 44
we have considered that the marked price of two balls is X i.e: 44 rupees.

The question is asking to find marked price of each ball

so, answer is 22 rupees

option B

Modulus(2a-3) = 3a+2, which can also be written as |2a-3| = 3a+2.

Modulus function  f(x) = |x| is defined as

|x| = x, for x>0,

|x| = -x, for x<0

So, we get two cases here,

Case (1):

2a-3>0

$$\Rightarrow a>\frac{3}{2}$$........................(1)

|2a-3| = 2a-3 = 3a+2

$$\Rightarrow a = -5$$

But from equation (1), The above value of a = -5 is not a possible case.

Case (2):

2a-3<0

$$\Rightarrow a<\frac{3}{2}$$....................(2)

|2a-3| = -(2a-3) = 3a+2

$$\Rightarrow a = \frac{1}{5}$$

This is a possible case, hence the value of $$a = \frac{1}{5}$$

From 32 litres, 4 litres is drawn out and is replaced with water.

Proportion of wine drawn = 4/32 = 1/8th of the total volume of the wine in the mixture.

When wine is drawn out for the second time, $$(1/8)\times (28) = 3.5$$ litres of wine will be drawn out.

Wine remaining in the jar = 28-3.5 = 24.5 litres

When wine is drawn out for the third time, $$(1/8)\times (24.5) =3.0625$$ litres of wine will be drawn out.

Wine remaining in the jar = 24.5 - 3.0625 = 21.4375 litres

Water in the jar = 10.5625 litres

Ratio of wine remaining in the jar to water remaining in the jar = 343:169

The geometric mean proportion between two numbers 'a' and 'b' is given by $$\sqrt{a\times b}$$

The given two numbers are 30 + $$\sqrt200$$ and 54 - $$\sqrt648$$

which are also equal to 10(3+$$\sqrt2$$) and 18(3-$$\sqrt2$$).

Hence the geometric mean proportion = $$\sqrt {10(3+\sqrt2)\times 18(3-\sqrt2)}$$ = $$\sqrt {180\times (3^2 - (\sqrt2)^2)}$$ = $$\sqrt {1260}$$ = $$6\times \sqrt35$$.

Given Anil is twice as good a student as Bharat

$$\Rightarrow$$ Efficiency  of  Anil : Efficiency  of  Bharat = 2:1

and also, Efficiency is inversely proportional to Time taken,

$$\Rightarrow$$ Time  taken  by  Anil : Time  taken  by  Bharat = 1:2...............................(1)

Given that Time taken by Anil is 30 min less than Bharat's time.

Let say, Time taken by Bharat be 't' minutes.

Then the time taken by Anil = t-30 minutes

Substituting these in equation (1), we get

$$\frac{t-30}{t} = \frac{1}{2}$$

$$\Rightarrow$$ t = 60  minutes.

Therefore the time taken by Anil and Bharat are 30 minutes and 60 minutes respectively.

Let Efficiency of Bharat be 'x', then Efficiency of Anil will be '2x'

$$\Rightarrow$$ Total Work = Efficiency\times Time taken = $$(2x)\times 30 (or) (x)\times 60 = 60x$$  units.

Efficiency when Anil and Bharat are working together = x+2x = 3x

Total Work = 60x units

Time taken(T) by Anil and Bharat together to complete the work = Total work/ Efficiency when Anil and Bharat work together

$$\Rightarrow T = \frac{60x}{3x}$$

$$\Rightarrow$$ T = 20  minutes.

Let the river start from point A and flows towards B, then turns left and reach at hill C. It goes around the hill counter-clockwise in a quarter circle to reach D, and then turns right finally to reach E.

Thus, river is flowing in east direction.

=> Ans - (C)

We are given that :Whenever Preeti’s father is in town, she abstains from school and goes to her aunt’s house.
Now option A says If Preeti has not abstained from school or she has not gone to her aunt’s house, it means that her father is not in town.
Now this can be inferred
Option B says  If Preeti has not abstained from school but her father is in town, then she will definitely go to her aunt’s house.This cannot be inferred as we cannot say she will surely  go to her aunt's house
option C says If Preeti has abstained from school but she has not gone to her aunt’s house, it means that her father is not in town. this can also be inferred as she has not gone to her aunt's house
So A and C both can ne inferred

Lima is seated at one of the extreme corners of the bench. Liyaqat is towards the right of Lima

=> Lima is at left end of row.

There is at least one person sitting between Lillian and Lima, => Now there are tow cases, when there is 1 person between them and when there are 2.

Liyaqat is towards the right of Lima but not towards the right of Lalit.

Case I : 

Case II : 

Thus, only statement which is definitely true is that there is at least one person between Lalit and Lima.

=> Ans - (D)

It is given that Cutty  plays Hockey.

Dolly plays either Basketball or Hockey, => Dolly plays Basketball.

Ali does not play Basketball or Cricket, => Ali plays Kabaddi.

Thus, only one left now is Benu plays Cricket.

=> Ans - (B)

On reading the Roads can be placed as :

We can say R8 R3 are the farthest south and farthest east .