Q1. What is the average weight of girls in the class?
I. Average weight of all the 60 students is 42 kg.
II. Average weight of boys is 43 kg
III. Total weight of all girls together is 1144 kg
(a) Any two of three
(b) All I, II & III
(c) I & II only
(d) II & III only
(e) Question cannot be answered even with information in all three statements.
I. Profit earned was 20%
II. Had 10% discount been offered on selling price the profit would have been Rs. 1200.
III. Cost price is Rs. 15000.
(a) Any two of the three
(b) Only I & II
(c) Only I I & III
(d) Only II & III
(e) None of these
Q3. What is the speed of the train?
I. Length of the platform is 150% of the length of the train.
II. The train crosses the platform in 25 seconds.
III. The train crosses the signal pole in 19 seconds.
(a) All I, II & III
(b) I and Either II or III
(c) Only II & III
(d) Any two of the three
(e) Question cannot be answered even with the information in all three statements.
Q4. What is the volume of the cylindrical tank?
I. Area of the base is X square metres.
II. Height of the tank is Y metres.
III. Diameter of the base is equal to height of the tank.
(a) Only I & II
(b) Only II & III
(c) Only I & III
(d) All I, II & III
(e) Any two of the three
Q5. Out of 5 women and 4 men a committee of three members is to be formed in such a way that at least one member is a women. In how many different ways can it be done?
(a) 80
(b) 84
(c) 76
(d) 96
(e) None of these
Q6. Arrange the letters of word AUCTION in such a way that the vowels always occur together. Find the number of ways?
(a) 576
(b) 48
(c) 144
(d) 30
(e) None of these
Q7. Two girls and 4 boys are to be seated in a row in such a way that the girls do no sit together. In how many different ways can it be done?
(a) 720
(b) 480
(c) 360
(d) 240
(e) None of these
Q8. In how many different ways can the numbers ‘256974’ be arranged, using each digit only once in each arrangement, such that the digits 6 and 5 are at the extreme ends in each arrangement?
(a) 48
(b) 720
(c) 36
(d) 360
(e) None of these
Q9. A basket contains 6 red, 5 green and 8 blue balls. If four balls are picked at random, what is the probability that all four of them are either red or any two out of the four are green?
(a) 5/1292
(b) 925/3876
(c) 359/1938
(d) 11/3876
(e) None of these
Q10. A bag contains 2 red, 3 green and 2 blue balls. 2 balls are to be drawn randomly. What is the probability that the balls drawn contain no blue ball?
(a) 5/7
(b) 10/21
(c) 2/7
(d) 11/21
(e) None of these
Q11. In a container there are 28 eggs out of which 8 eggs are rotten. If two eggs are chosen at random, what will be the probability that atleast one egg is rotten?
(a) 94/189
(b) 95/187
(c) 93/189
(d) 97/189
(e) None of these
Q12. A box contains 4 black balls, 3 red balls and 5 green balls. 2 balls are drawn from the box at random. What is the probability that both the balls are of the same colour?
(a) 47/68
(b) 1/6
(c) 19/66
(d) 2/11
(e) None of these
Directions (13-15): What should come in place of the question mark (?) in the following number series?
Q13. 586, 587, 586, 581, 570, ?, 522
(a) 545
(b) 543
(c) 551
(d) 557
(e) None of these
Q14. 4000, 2008, 1012, ?, 265, 140.5, 78.25
(a) 506
(b) 514
(c) 520
(d) 512
(e) None of these
Q15. 50, 60, 75, 97.5, ?, 184.275, 267.19875
(a) 120.50
(b) 130.50
(c) 131.625
(d) 124.25
(e) None of these
Solution:
S1. Ans.(b)
Sol. I) Total weight of 60 students = 42×60=2520 kg.
II) Average weight of boys = 43 kg.
III) Total weight of all girls = 1144 kg.
So, total weight of all boys = 2520 – 1144
= 1376
So, no. of boys = 1376/43=32
No. of girls = 60 – 32 = 28
& average weight of girls = 1144/28=40.86 kg.
⇒Hence, all statements are necessary.
S2. Ans.(a)
Sol. From I & II,
Let CP = x
S.P = 6x/5
Now, New S.P = 6x/5×90/100=54x/50
⇒54x/50-x=1200
⇒x=15000
∴ SP. = 18000
& from III & I, we can obtain selling price.
& from II & III,
Let S.P. = x
When 10% discount,
S.P. = 9x/10
∴9x/10-15000=1200
⇒x=18000
Thus, any the three statements is required.
S3. Ans.(e)
Sol. ∵ Length of platform or train is not given.
So, we can’t answer the question with the information given.
S4. Ans.(e)
Sol. To get volume of cylinder, we need height and radius.
So, from any two of three statement, we can get answer.
S7. Ans.(b)
Sol. Total possible arrangement = (2+4)!=6!=720
When two girls sit together,
2!×5!=240
Required answer = 720–240=480
S8. Ans.(a)
Sol. Case I : - 6 _ _ _ _ 5
4 empty place can be filled by 2, 9, 7, 4.
So, ways = 4! = 24
Case II: - 5 _ _ _ _ 6
Then possible no. of ways = 4! = 24
Total arrangements = 24 + 24 = 48
S13. Ans.(c)
Sol. Series is : -
586+1=587
587+(1-2)=586
586+(-1-4)=581
581+(-5-6)=570
570+(-11-8)=551
S14. Ans.(b)
Sol. Series is ÷2+8,÷2+8,÷2+8…………
So, 1012 ÷ 2 + 8 = 514
S15. Ans.(c)
Sol. The pattern is
50×1.2=60
60×1.25=75
75×1.3=97.5
97.5×1.35=131.625
131.625×1.4=184.275
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