Elitmus previous questions set - 5

Elitmus previous questions set - 5

1. Two identical cubes if one of them is painted pink on its 4 sides and blue on the remaining two side then how many faces painted pink to other cube so that probability of getting the same color is 1/3 when we roll both the cubes.

Explanation:
First cube has got 4 pink sides and 2 black sides.
Let the other cube got x sides pink and (6 - x) sides black.
Now when we roll both the dice, we can either pink on both cubes or black on both cubes.
Probability = 46×x6+26×6−x6=13${\displaystyle \frac{4}{6}}\times {\displaystyle \frac{x}{6}}+{\displaystyle \frac{2}{6}}\times {\displaystyle \frac{6-x}{6}}={\displaystyle \frac{1}{3}}$
=4x+12−2x36=13$={\displaystyle \frac{4x+12-2x}{36}}={\displaystyle \frac{1}{3}}$
⇒x=0$\Rightarrow x=0$
So second cube should not have any pink faces at all.

2. In a right angled triangle, two sides are consecutive whole number in which one side is hypotenuse. what could be the possible length of third side?
1. 360
2. 361
3. 362
4. none of these
Answer: 2
Explanation:
Pythagorean triplets are generated with each "odd number" greater than 1 by using a formula.
If n is an odd number, then Pythagorean triplet = n,n2−12,n2+12$n,{\displaystyle \frac{n^2-1}{2}},{\displaystyle \frac{n^2+1}{2}}$.
Here 361 is an odd number.  So the triplet is 361, 65160, 65161.

3. Heinz produces tomato puree by boiling tomato juice. The tomato puree has only 20% water while the tomato juice has 90% water. How many liters of tomato puree will be obtained from 20 litres of tomato juice?
a. 2 liters
b. 2.4 liters
c. 2.5 liters
d. 6 liters
Answer:
Explanation:
In each of the solutions, there is a pure tomato component and some water.  So while boiling, water evaporates but tomato not. So we equate tomato part in the both equations.
⇒$\Rightarrow$ 10%(20) = 80%(x)
⇒$\Rightarrow$ x = 2.5 liters.

4. x,y are odd and z is even then ((x^2+y^2)z^2)/8 is
a. even
b. odd
c. either even or odd
d. fraction
Explanation: c
As x, y are odd x2+y2$x^2+y^2$ is always even. Now if z is a multiple of 4, then z2$z^2$ is divisible by 8, then the equation is even.  if z is a not a multiple of 4, but only a multiple of 2, then z2$z^2$ is not completely divisible as it contains only two 2's and other two is cancelled in x2+y2$x^2+y^2$ which results in an odd number.
(32+52)428=34×168=34×2${\displaystyle \frac{\left(3^2+5^2\right)4^2}{8}}={\displaystyle \frac{34\times 16}{8}}=34\times 2$
(32+52)628${\displaystyle \frac{\left(3^2+5^2\right)6^2}{8}}$ = 34×368=17×9${\displaystyle \frac{34\times 36}{8}}=17\times 9$

5. In the formula of converting temperature from Celsius to Fahrenheit F=9/5C+32, How many integer values(not fractional) of F will be there that lies between 100 to 200 for integer values of C.
Explanation:
F=95C+32$F={\displaystyle \frac{9}{5}}C+32$
As F needs to be integer, then C should be a multiple of 5. First integer value of F for C = 5 is 41, next value for C =10 is 50 and so on.
The values of F are in A.P with common difference of 9. They are in the format of 41 + 9n.
The first value of F which is greater than 100 is for n = 7 which is 104.
The last value of F which is less than 200 is for n = 17, which is 194.
Total values are 194−1049+1${\displaystyle \frac{194-104}{9}}+1$ = 11

6. The product of digit is a Factor of a two digit number.  Number of such digit are:
a. 3
b. 5
c. 9
d. 27
Answer: b
Explanation:
Let the number be xy. So 10x+yxy=k${\displaystyle \frac{10x+y}{xy}}=k$.  Here k is some interzer.
⇒$\Rightarrow$ 10x + y = kxy
⇒$\Rightarrow$ x(10 - ky) = - y
⇒$\Rightarrow$ x(ky - 10) = y
So x is a factor of y. The possibilities are,
11, 1×1=1; 12 , 1×2=2; 15 ,1×5=5; 24 ,2×4=8; 36 , 3×6=18

7. Data sufficiency question.
is x>y ?
1. 5x+15y=40
2.7x+21y=56 
Explanation:
Statement 1 has three solutions,(8, 0), (5, 1), (2, 2) but we cannot say precisely about the relationship
Statement 2 has three solutions, (8, 0), (5, 1), (2, 2) but we cannot say about the relationship.
So data insufficient. 

Infosys Previous questions

Infosys Previous questions

1. What is the 8th term in the series 1, 4, 9, 18, 35, 68, . . . 

Sol:
1, 4, 9, 18, 35, 68,  . . .
The pattern is
1 = 2¹ – 1
4 = 2² – 0
9 = 2³ + 1
18 = 2⁴ + 2
35 = 2⁵ + 3
68 = 2⁶ + 4
So 8th term is 2⁸ + 6 = 262

2. USA + USSR = PEACE ; P + E + A + C + E = ?
Sol:
3 Digit number + 4 digit number = 5 digit number. So P is 1 and U is 9, E is 0.
Now S repeated three times, A repeated 2 times. Just give values for S. We can easily get the following table.

USA =  932
USSR = 9338
PEACE =  10270
P + E + A + C + E  = 1 + 0 + 2 + 7 + 0  = 10

3. In a cycle race there are 5 persons named as J, K, L, M, N participated for 5 positions so that in how many number of ways can M make always before N?
Sol:
Say M came first.  The remaining 4 positions can be filled in 4! = 24 ways.
Now M came in second.  N can finish the race in 3rd, 4th or 5th position. So total ways are 3 x 3! = 18.
M came in third. N can finish the race in 2 positions. 2 x 3! = 12.
M came in second. N can finish in only one way. 1 x 3! = 6
Total ways are 24 + 18 + 12 + 6 = 60.

Shortcut: 
Total ways of finishing the race = 5! = 120. Of which, M comes before N in half of the races, N comes before M in half of the races. So 120 / 2 = 60.

4. If POINT + ZERO = ENERGY, then E + N + E + R + G + Y = ?
Sol:
4 digit number + 5 digit number = 6 digit number. So E = 1, P = 9, N = 0
Observe R + 0 = G. But R = G not possible. 1 + R = G possible. So R and G are consecutive. G > R.
1 + I = R, So I and R are consecutive. R > I. i.e., G > R > I. and G, R, I are consecutive. Now O + T should give carry over and O + Z also give carry over. So O is bigger number.  Now take values for G, R, I as 8, 7, 6 or 7, 6, 5 etc. and do trial and error.

POINT = 98504, ZERO = 3168 and ENERGY = 101672.
So E + N + E + R + G + Y = 1 + 0 + 1 + 6 + 7 +2 = 17

5. There are 1000 junior and 800 senior students in a class.  And there are 60 sibling pairs where each pair has 1 junior and 1 senior.1 student is chosen from senior and 1 from junior randomly.What is the probability that the two selected students are from a sibling pair?
Sol:
Junior student = 1000
Senior student = 800
60 sibling pair = 2 x 60 = 120 student
Probability that 1 student chosen from senior = 800
Probability that 1 student chosen from junior = 1000
Therefore,1 student chosen from senior and 1 student chosen from junior
n(s) = 800 x 1000 = 800000
Two selected student are from a sibling pair
n(E) = ¹²⁰C₂ = 7140
Therefore
P(E) = n(E)/n(S) = ⁷¹⁴⁰⁄₈₀₀₀₀₀

6. SEND + MORE = MONEY. Then what is the value of M + O +  N  + E + Y ?
Sol:
Observe the diagram.  M = 1. S + 1 = a two digit number. So S = 1 and O cannot be 1 but 0. Also E and N are consecutive. Do trial and error.

SEND   = 9567, MORE = 1085, MONEY =  10652
SO M + O + N + E + Y = 1 + 0 + 6 +  5 + 2 = 14

7. A person went to shop and asked for change for 1.15 paise.  But he said that he could not only give change for one rupee but also for 50p, 25p, 10p and 5p. What were the coins he had ?
Sol:
50 p : 1 coin, 25 p : 2 coins, 10 p: 1 coin, 5 p : 1 coin, Total: 1.15 p

8. 1, 1, 2, 3, 6, 7, 10, 11, ?
Sol:
The given pattern is (Prime number - consecutive numbers starting with 1).
1 = 2 – 1
1 = 3 – 2
2 = 5 – 3
3 = 7 – 4
6 = 11 – 5
7 = 13 – 6
10 = 17 – 7
11 = 19 – 8
14 = 23 – 9