CAT 2018 – Slot 2 – Quantitative Aptitude – On a triangle ABC, a circle with diameter BC is drawn -

CAT 2018 – Slot 2 – Quantitative Aptitude – On a triangle ABC, a circle with diameter BC is drawn

Q. 1: On a triangle ABC, a circle with diameter BC is drawn, intersecting AB and AC at points P and Q, respectively. If the lengths of AB, AC, and CP are 30 cm, 25 cm, and 20 cm respectively, then the length of BQ, in cm, is

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As CP is perpendicular to AB and BQ is perpendicular to AC. So

AB×CP=AC×BQ

30×20=25×BQ

BQ = 24 cm

Q. 2: A chord of length 5 cm subtends an angle of 60° at the centre of a circle. The length, in cm, of a chord that subtends an angle of 120° at the centre of the same circle is
1. 8
2. 6√2
3. 5√3
4. 2

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In triangle ODA, OA=AD cosec 30=5

So if the angle AOB is 120 degree, then angle AOD will be 120/2=60

In the case length of chord = 2×OA Sin 60=5√3

Q. 3: Let f(x)=max{5x, 52-2x^2}, where x is any positive real number. Then the minimum possible value of f(x) is?

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For f(x) to be minimum , 5 = 52 − 2^2

2^2+5 −52 =0

−42+13=0

= 4

Thus minimum value of f(x) = 5x = 5*4 = 20

Q. 4: A 20% ethanol solution is mixed with another ethanol solution, say, S of unknown concentration in the proportion 1:3 by volume. This mixture is then mixed with an equal volume of 20% ethanol solution. If the resultant mixture is a 31.25% ethanol solution, then the unknown concentration of S is
1. 52%
2. 50%
3. 55%
4. 48%

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Let the volume of 20% ethanol solution in first mixtures = x so

Volume of S = 3x

Total volume of first solution = 4x

Total volume of final solution =2×4x=8x

Volume of ethanol solution in final mixture = x + 4x = 5x ,

So volume of S in final solution = 3x

Thus (31.25-20)/(s-31.25) = 3x/5x = 3/5

56.25=3s-93.75

3s=150

s=50%

Q. 5: A tank is emptied everyday at a fixed time point. Immediately thereafter, either pump A or pump B or both start working until the tank is full. On Monday, A alone completed ?lling the tank at 8 pm. On Tuesday, B alone completed filling the tank at 6 pm. On Wednesday, A alone worked till 5 pm, and then B worked alone from 5 pm to 7 pm, to fill the tank. At what time was the tank ?lled on Thursday if both pumps were used simultaneously all along?
1. 4:36 pm
2. 4:12 pm
3. 4:24 pm
4. 4:48 pm

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Let pump A alone can fill the tank in t hours so time taken by pump B alone = t-2 hours

As per question , (t-3)/t+2/(t-2)=1

t^2-3t+6=t^2-2t

Or t=6

So the time at which pumps tank is emptied = 8 pm – 6 hours = 2 pm

Time taken by both pumps together to fill the tank =(6×4)/(6+4)=2.4 hours=2 hour 24 minutes

Thus tank will be filled by 2 pm + 2 hour 24 minutes=4:24 pm

Checkout Other Questions of CAT 2018 Slot 2 Paper:

Verbal Ability : | Q.01- Q.05 | Q.06- Q.9 | Q.10- Q.14 | Q.15- Q.19 | Q.20- Q.24 | Q.25- Q.29 | Q.30 – Q.34 |

Logical Reasoning : | Q.01- Q.04 | Q.05- Q.08 | Q.09- Q.12 | Q.13- Q.16 | Q.17- Q.20 | Q.21- Q.24 | Q.25 – Q.28 | Q.29 – Q.32 |

Quantitative Aptitude: | Q.01- Q.05 | Q.06- Q.10 | Q.11- Q.15 | Q.16- Q.20 | Q.21- Q.25 | Q.26- Q.30 | Q.31 – Q.34 |