21. The hour hand lies between 3 and 4. Tthe difference between hour and minute hand is 50 degree.What are the two possible timings?
Sol:
The angle between the hour hand and minute hand at a given time H:MM is given by
? = 30×H 211×MM
The time after H hours, hour hand and minute hand are at
MM = | 211×((30×H)±?) |
given H = 3, MM = 50
Substituting the above values in the formula
? = 8011, 28011
22. Jack and Jill went up and down a hill. They started from the bottom and Jack met Jill again 20 miles from the top while returning. Jack completed the race 1 min a head of Jill. If the hill is 440 miles high and their speed while down journey is 1.5 times the up journey. How long it took for the Jack to complete the race ?
Sol:
Assume that height of the hill is 440 miles.
Let speed of Jack when going up = x miles/minute
and speed of Jill when going up = y miles/minute
Then speed of Jack when going down = 1.5x miles/minute
and speed of Jill wen going up = 1.5y miles/minute
Case 1 :
Jack met jill 20 miles from the top. So Jill travelled 440 20 = 420 miles.
Time taken for Jack to travel 440 miles up and 20 miles down = Time taken for Jill to travel 420 miles up
440x+201.5x=420y
681.5x=420y
68y = 63x
y = 63×68 —(1)
Case 2 : Time taken for Jack to travel 440 miles up and 440 miles down = Time taken for Jill to travel 440 miles up and 440 miles down 1
440x+4401.5x=440y+4401.5y 1
440×53(1y?1x)=1—–(2)
Substitute (2) in (1) we get
x = 440×5×53×63
t = 440×53(1x)
t = 12.6min
23. Data Sufficiency question:
A, B, C, D have to stand in a queue in descending order of their heights. Who stands first?
I. D was not the last, A was not the first.
II. The first is not C and B was not the tallest.
Sol:
D because A is not first neither C and B is not the tallest person. The only person will be first is D.
So option (C). We can answer this question using both the statements together.
24. One of the longest sides of the triangle is 20 m. The other side is 10 m. Area of the triangle is 80 m2. What is the another side of the triangle?
Sol:
If a,b,c are the three sides of the triangle.
Then formula for Area = (s(sa)×(sb)×(sc))?????????????????????
Where s = (a+b+c)2=12×(30+c)
[Assume a = 20 ,b = 10]
Now,
Check the options.
25. Data Sufficiency Question:
a and b are two positive numbers. How many of them are odd?
I. Multiplication of b with an odd number gives an even number.
II.a2 b is even.
Sol:
From the 1st statement b is even, as when multiplied by odd it gives even
a2 b = even
? a is even
Here none of a and b are odd
26. Mr. T has a wrong weighing pan. One arm is lengthier than other. 1 kilogram on left balances 8 melons on right, 1 kilogram on right balances 2 melons on left. If all melons are equal in weight, what is the weight of a single melon.
Sol:
Let additional weight on left arm be x.
Weight of melon be m
x + 1 = 8 x m – – – – – – (1)
x + 2 x m = 1 – – – – – – (2)
Solving 1 & 2 we get.
Weight of a single Melon = 200 gm.
27. a, b, b, c, c, c, d, d, d, d, . . . . . . Find the 288th letter of this series.
Sol:
Observe that each letter appeared once, twice, thrice ….
They form an arithmetic progression. 1+2+3……
We know that sum of first n natural numbers = n(n+1)2
So n(n+1)2 ? 288
For n = 23, we get 276. So for n = 24, the given series crosses 288.
Ans is X
28. There are three trucks A, B, C. A loads 10 kg/min. B loads 13 1/3 kg/min. C unloads 5 kg/min. If three simultaneously works then what is the time taken to load 2.4 tones?
Sol:
Work done in 1 min =10 + 403 5= 553 kg/min
For 1 kg = 3/55 min
For 2.4 tonnes = 3/55 x 2.4 x 1000 = 130 mins = 2hrs 10min
29. A person is 80 years old in 490 and only 70 years old in 500 in which year is he born?
a) 400
b) 550
c) 570
d) 440
Sol:
He must have born in BC 570
Hence in BC 500 he will be 70 years
And in BC 490 he will be 80 years
30. Lucia is a wonderful grandmother and her age is between 50 and 70. Each of her sons have as many sons as they have brothers. Their combined ages give Lucia’s present age.what is the age?
Sol:
The question basically states that if Lucia were to have say 10 sons, then each son would have 9 sons (Lucia’s grandsons since each son has 9 brothers). So the total in this case would be 9×10 grandsons + 10 sons = 100.
Let us assume Lucia has got x sons. Now each son has (x – 1) sons. So total = x + (x – 1) x. For x = 8 we get 64 which is in between 50 and 60. ( 7 x 8 grandsons + 8 sons = 64 )
31. A family X went for a vacation. Unfortunately it rained for 13 days when they were there. But whenever it rained in the mornings, they had clear afternoons and vice versa. In all they enjoyed 11 mornings and 12 afternoons. How many days did they stay there totally?
Sol:
Clearly 11 mornings and 12 afternoons = 23 half days
since 13 days raining means 13 half days.
so 23 13 =10 half days ( not affected by rain )
so 10 half days = 5 full days
Total no. of days = 13 + 5 = 18 days.
32. Find the unit digit of product of the prime number up to 50 .
Sol:
Prime number up to 50 are
2,3,5,7,11,…,43,47
Product = 2×3×5×7×11×???×43×47
There’s a term 2×5=10
So unit digit of product = 0
33. Complete the series..
2 2 12 12 30 30 ?
Sol:
Answer is 56.
It follows the series as:
1 x 2 = 2
2 x 1 = 2
3 x 4 = 12
4 x 3 = 12
5 x 6 = 30
6 x 5 = 30
7 x 8 = 56
This is the required number for the series.
34. An escalator is descending at constant speed. A walks down and takes 50 steps to reach the bottom. B runs down and takes 90 steps in the same time as A takes 10 steps. How many steps are visible when the escalator is not operating?
Sol:
Lets suppose that A walks down 1 step / min and
escalator moves n steps/ min
It is given that A takes 50 steps to reach the bottom
In the same time escalator would have covered 50n steps
So total steps on escalator is 50 + 50n.
Again it is given that B takes 90 steps to reach the bottom and time
taken by him for this is equal to time taken by A to cover 10 steps i.e
10 minutes. So in this 10 min escalator would have covered 10n steps.
So total steps on escalator is 90 + 10n
Again equating 50 + 50n = 90 + 10n we get n = 1
Hence total number of steps on escalator is 100.
35. How many ways can one arrange the word EDUCATION such that relative positions of vowels and consonants remains same?
Sol:
The word EDUCATION is a 9 letter word with none of letters repeating
The vowels occupy 3,5,7th & 8th position in the word & remaining five positions are occupied by consonants.
As the relative position of the vowels & consonants in any arrangement should remain the same as in the word EDUCATION
The four vowels can be arranged in 3rd,5th,7th & 8th position in 4! ways.
similarly the five consonants can be arranged in 1st ,2nd ,4th, 6th & 9th position in 5! ways
Hence the total number of ways = 5!×4!=120×24=2880
