eLitmus sample papers and previous year questions are given here. For the eLitmus exam, you need to practice eLitmus sample questions. This will help you familiarize with the type of questions asked in each section. Hence, we are providing with some eLitmus Sample papers and sample questions that have occurred in previous exams.
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eLitmus Sample Papers – Quantitative Aptitude
1) Find the number of ways you can fill a 3*3 grid (with 4 corners defined as a,b,c,d) if you have 3 white marbles and 6 black marbles
a) 9C3 b) 6C3 c) 9C3+6C3 d) (9C3+6C3)/3!
We can choose any 3 places for white marbles in 9c3 and remaining places are left for black marbles; we do not have to arrange them because they all are identical.
2) How many values of c in the equation x^2-5x+c result in rational roots which are integers.
a) 1 b) 3 c) 6 d) infinite
By the quadratic formula, the roots of x^2-5x+c are -b + sqrt(b^2-4ac)/2a
To get rational roots, 25−4c25−4c should be square of an odd number. Because 5 + odd only divided by 2 perfectly. Now let 25 – 4c = 1, then c = 6
If 25 – 4c = 9, then c = 4
If 25 – 4c = 25, then c = 0 and so on…
So infinite values are possible.
3) If 1/a + 1/b + 1/c=1/(a+b+c) where a+b+c#0,abc#0 what is the value of (a+b)(b+c)(c+a)?
a) equals 0
b) greater than 0
c) less than 0
d) cannot be determined
=> a2b+ab2+ac2+a2c+b2c+bc2+2abc=0 = (a+b)(b+c)(c+a)=(ab+ac+b2+bc)(c+a)
=abc+ac2+b2c+bc2+a2c+a2b+b2a+abc = 0
4) Einstein walks on an escalator at a rate of 5steps per second and reaches the other end in 10 sec. while coming back, walking at the same speed he reaches the starting point in 40secs. What is the number of steps on the escalator?
Escalator problems are similar to boats and streams problems. If we assume man’s speed as ‘a m/s’ and escalator speed as ‘b m/sec’ then while going up man’s speed becomes ‘a -b’ and while coming down ‘a + b’.
In this question, Let the speed of escalator be b steps per sec. And the length of escalator be L. Einstein’s speed = 5 steps/ sec
While going down, L/5+x=10 ⇒⇒ L = 50 + 10x
While coming up, L/5−x=40 ⇒⇒ L = 200 – 40x
Multiply the first equation by 4, and add to the second, we get L = 80
5) How many six digit number can be formed using the digits 1 to 6, without repetition, such that the number is divisible by the digit at unit’s place
Divisible by 1 and 1 at the unit place:
_ _ _ _ _ 1 : This gives us a total of 5 x 4 x 3 x 2 x 1 = 120 numbers.
Divisible by 2 and 2 at the unit place:
_ _ _ _ _ 2 : This gives us a total of 5 x 4 x 3 x 2 x 1 = 120 numbers.
Divisible by 3 and 3 at the unit place:
_ _ _ _ _ 3 : Since any number will have all the digits from 1 to 6 and the sum 1 + 2 + 3 + 4 + 5 + 6 = 21 is divisible by 3. This gives us total of 5 x 4 x 3 x 2 x 1 = 120 numbers.
Divisible by 4 and 4 at the unit place:
_ _ _ _ _ 4 : Here, there are two cases
i) _ _ _ _ 2 4 : This gives 4 x 3 x 2 x 1 = 24 numbers.
ii) _ _ _ _ 6 4 : This gives 4 x 3 x 2 x 1 = 24 numbers.
This gives us total of 24 + 24 = 48 numbers.
Divisible by 5 and 5 at the unit place:
_ _ _ _ _ 5 : This gives us a total of 5 x 4 x 3 x 2 x 1 = 120 numbers.
Divisible by 6 and 6 at the unit place:
_ _ _ _ _ 6 : As all 6 digit numbers formed with 1 to 6 digits(without repetition) are divisible by 3 and numbers with 6 at the unit place are even. This gives us total of 5 x 4 x 3 x 2 x 1 = 120 numbers.
None of these cases will have numbers overlapping with each other.
So, Total numbers = 120 + 120 + 120 + 48 + 120 + 120 = 648
6) The owner of a local jewel store hired 3 watchmen to guard his diamonds but a thief still got in and stole some diamonds. On the way out, the thief met all the watchmen, one at a time. To each of them, he gave half the diamonds he had then, and 2 more besides. He escaped with one diamond. How many did he steal originally?
At last, the thief is left with one diamond. Hence, the number of diamonds before he gave some diamonds to the third watchman,
=x-((x/2) +2) = 1; Or, (x-4)/2 = 1; or, x = 6.
Hence, he had 6 diamonds before he gave 5 to the third watchman.
Similarly the number of diamonds before giving to the second watchman,
(x-4)/2=6; Or, x = 16. And number of diamonds before giving to the first watchman,
(x-4)/2 = 16; Or, x = 36. Therefore, the thief has stolen 36 diamonds originally.
7) If the price of petrol increases by 25% and Kevin intends to spend only an additional 15% on petrol, then by what percentage must he reduce the quantity of petrol purchased?
d) None of these
After the increase by 25%, price of 1 Litre petrol = 100 × (100+25)/100=Rs.125. Since Kevin spends an additional 15% on petrol. The amount spent by Kevin = 100 × (100+15)/100=Rs.115.
Hence Quantity of petrol that he can purchase = 115/125 Litre. Quantity of petrol reduced = (1−115/125) Litre.
Percentage Quantity of reduction = (1−115/125)/1×100=10/125×100=10/5×4=2×4=8%
8) The circle O having a diameter of 2 cm, has a square inscribed in it. Each side of the square is then taken as a diameter to form 4 smaller circles O’. Find the total area of all four O’ circles which is outside the circle O.
Area of Circle O = pi*(1) ^2 = pi, Now the diameter of the circle is also the diagonal of the square. Hence each side of the square will be sqrt (2). =>Area of square=2.
Since each side of the square is also the diameter of other 4 circles. Hence summation of the area of 4 circles=2*pi……….. (1)
If you have drawn its fig you’ll find that to obtain the required answer you have to subtract the area of 4 semi-circles formed on the side of the square from the each of the small portion outside the square. To get that area of small portion =area of circle O-area of square =pi-2……. (2)
This small portion has to be subtracted from the four semi-circles. Hence, area of 4 semi-circles=2*pi/2= pi…… [from (1)]
Required answer = total area of 4 semi-circles – area of small portion (from (2))
=pi-(pi-2) = 2
9) A can do a piece of work in 24 days and B in 20 days but with the help of C they finished the work in 8 days. C alone can do the work in how many days?
a) 25 days
b) 28 days
c) 30 days
d) 24 days
You can take the total work to be equal to 120 units (the LCM of 24, 20 & 8). That implies A does 120/24 = 5 units a day, B does 120/20 = 6 units a day. Together they finished the work in 8 days means they are doing 120/8 = 15 units a day. Let the units done by C per day be = c. Now as per the statement 5 + 6 + c = 15 ⇒ c = 4 units. Now if C does 4 units a day, he can finish the work in 120/4 = 30 days.
10) A runs 25% faster than B and is able to give him a start of 7m to end a race in the dead heat. What is the length of the race?
a) 10 m
b) 45 m
c) 35 m
d) 25 m
A runs 25% as fast as B. i.e., if B runs 100 m in a given time, A will run 125 m in the same time.
In other words, if A runs 5 m in a given time, then B will run 4 m in the same time. Therefore, if the length of a race is 5 m, then A can give B a start of 1 m (A can allow B to start 1 ahead of the starting point) so that they finish the race in a dead heat.
Ratio of length of start given: length of race: 1 : 5 In this question, we know that the start given is 7m. Hence, the length of the race will be 7 * 5 = 35 m.
eLitmus Sample Papers – Logical Reasoning
1) X Z Y + X Y Z = Y Z X. Find the three digits
a) X=9, Y=5, Z=4
b) X=5, Y=4, Z=9
c) X=4, Y=5, Z=9
d) X=4, Y=9, Z=5
2nd column, Z + Y = Z shows a carry so, Z + Y + 1 = 10 + Z ⇒ Y = 9
1st column, X + X + 1 = 9 ⇒⇒ X = 4 so, Z = 5
459 + 495 = 954
X = 4, Y = 9, Z = 5
2) MAC + MAAR = JOCKO, find the value of 3A + 2M + 2C.
M A C
+ M A A R
J O C K O
Here J is carry, J=1 when J=1, O=0 with carry 1 and M=9 C+R=O à 0 with carry 1. So, C=2 and R=8 M+A=C à 2 with carry 1, A=3, A+A+1= K, 3+3+1=K=7, 932+9338=10270 so, finally A = 3, M = 9, C = 2, = 3A + 2M + 2C = 9 + 18 + 4 = 31
3) W W W + D O W N = E R R O R. Find the value of D + O + W + N = ?
10030 — Substitute all the values we get 22.
4) P L A Y S + W E L L = B E T T E R. Find P + B + W = ?
a) 18 b) 14 c) 17 d) 12
Substitute the values we get, 18
eLitmus Sample Papers – Verbal Ability
1) Corruption is ____ in our society; the integrity of even senior officials is ____.
a) Rife- suspectful
c) Endangered- disputed
d) Pervasive- intact
The semicolon suggests that the second part expands upon the first part. So, if corruption is rife (common), then we will doubt the integrity of the officials. Their integrity will be suspect (doubtful). (Pervasive = spreading everywhere; rife = common)
Directions for questions: 17 – 19:
The Indian middle class consist of so many strata that it defies categorization under a single term class, which would imply a considerable degree of homogeneity. Yet two paradoxical features characterize its conduct fairly uniformly; extensive practice and intensive abhorrence of corruption. In the several recent surveys of popular perceptions of corruptions, politicians of course invariably and understandably top the list, closely followed by bureaucrats, policemen, lawyers, businessmen and others. The quint essential middle class. If teachers do not figure high on this priority list, it is not for lack of trying, but for lack of opportunities. Over the years, the sense of shock over acts of corruption in the middle class has witnessed a steady decline, as its ambitions for a better material life have soared but the resources for meeting such ambitions have not kept pace. What is fascinating, however, is the intense yearning of this class for a clean corruption less politics and society, a yearning that has again and again surfaced with any figure public or obscure, focus on his mission of eradicating corruption. Even the repeated failure of this promise on virtually every man’s part has not subjected it to the law of diminishing returns.
2) This yearning, over the years, has
3) Who figure on top of the list of corruption?
4) The Indian Middle class is
5) Arrange the sentences into a paragraph:
Good literary magazines have always been good because of their editors.
A) Furthermore, to edit by committee, as it were, would prevent any magazine from finding its own identity.
B) The more quirky and idiosyncratic they have been, the better the magazine is, at least as a general rule.
But the number of editors one can have for a magazine should also be determined by the number of contributions to it.
C) To have four editors for an issue that contains only seven contributions, it is a bit silly to start with.
D) However, in spite of this anomaly, the magazine does acquire merit in its attempt to give a comprehensive view of the Indian literary scene as it is today.
6) In the Middle Ages, the ____ of the great cathedrals did not enter into the architects’ plans; almost invariably a cathedral was positioned haphazardly in ____ surroundings.
a) situation – incongruous
b) location – apt
c) ambience – salubrious
d) durability – convenient