# 1. The figure shown can be folded into the shape of a cube.  In the resulting cube, which of the lettered faces is opposite the face marked x?

a. c
b. a
c. d
d. b
Ans: a
Explanation: If you fold the above picture at the dotted lines, X and C are opposite to each other.

2. In how many ways a team of 11 must be selected from 5  men and 11 women such that the team must comprise of not more than 3 men?
a. 1565
b. 1243
c. 2256
d. 2456
Ans: C
Explanation;
The team may consist of 0 men + 11 women, 1 men + 10 women, 2 men + 9 women, or 3 men + 8 women.
So Number of ways are = 11C11+5C1×11C10+5C2×11C9+5C3×11C8 = 2256

3. Given that 0 < a < b < c < d, which of the following the largest ?
a.(c+d) / (a+b)
b.(a+d) / (b+c)
c.(b+c) / (a+d)
d.(b+d) / (a+c)
Sol: A
Explanation: Take a = 1, b = 2, c = 3, d = 4. option A is clearly true.

4. Eesha bought 18 sharpeners for Rs.100.  She paid 1 rupee more for each white sharpener than for each brown sharpener.  What is the price of a white sharpener and how many white sharpener did she buy ?
a. Rs.5, 10
b. Rs.6, 10
c. Rs.5, 8
d. Rs.6, 8
Sol: B
Explanation: Just check the options. If she bought 10 white sharpeners at Rs.6 per piece, She has spent Rs.60 already. And with the remaining Rs.40, she bought 8 brown sharpeners at 40/8 = Rs.5 which is Rs.1 less than White sharpener.

5.

The fourteen digits of a credit card are to be written in the boxes shown above.  If the sum of every three consecutive digits is 18, then the value of x is :
a. 3
b. cannot be determined from the given information.
c. 2
d. 1
Sol : A
Explanation:
Let us assume right most two squares are a , b
Then Sum of all the squares = 18 x 4 + a + b .......... (1)
Also Sum of the squares before 7 = 18
Sum of the squares between 7, x = 18
and sum of the squares between x , 8 = 18
So  Sum of the 14 squares = 18 + 7 + 18 + x + 18  + 8 + a + b (2)
Equating 1 and 2 we get x = 3

6. Four people each roll a four die once.  Find the probability that at least two people will roll the same number ?
a. 5/18
b. 13/18
c. None of the given choices
d. 1295/1296
Sol: B
Explanation:
The number of ways of rolling a dice where no two numbers probability that no one rolls the same number = 6 x 5 x 4 x 3
Now total possibilities of rolling a dice = 64
The probability that a no one gets the same number = 6×5×4×364=518
So the probability that at least two people gets same number = 1518=1318

7. Jake can dig a well in 16 days.  Paul can dig the same well in 24 days.  Jake, Paul and Hari together dig the well in 8 days.  Hari alone can dig the well in
a. 96 days
b. 48 days
c. 32 days
d. 24 days
Sol:
Explanation: Simple one. Let the total work to be done is 48 meters. Now Jake can dig 3 mts, Paul can dig 2 mts a day. Now all of them combined dug in 8 days so per day they dug 48/8 = 6 mts. So Of these 8 mts, Hari capacity is 1 mt.
So he takes 48 /1 = 48 days to complete the digging job.

8. Eesha bought 18 sharpeners for Rs.100.  She paid 1 rupee more for each white sharpener than for each brown sharpener.  What is the price of a white sharpener and how many white sharpener did she buy ?
a. Rs.5, 10
b. Rs.6, 10
c. Rs.5, 8
d. Rs.6, 8
Ans:
Explanation: This question can be solved easily by going through options.
A. White sharpener total cost: Rs.5 x 10 = Rs.50.  Brown sharpeners cost = Rs.4 x 8 = 32. Total cost is only Rs.82. Wrong option.
B. White sharpener total cost: Rs.6 x 10 = Rs.60.  Brown sharpeners cost = Rs.5 x 8 = 40. Total cost is Rs.100. Correct option.

9. The sum of the digits of a three digit number is 17, and the sum of the squares of its digits is 109.  If we subtract 495 from the number, we shall get a number consisting of the same digits written in the reverse order.  Find the number.
a. 773
b. 683
c. 944
d. 863
Ans: D
Explanation: Check options.  Sum of the squares should be equal to 109. Only Options B and D satisfying. When we subtract 495, only 863 becomes 368.

10. Mark told John "If you give me half your money I will have Rs.75.  John said, "if you give me one third of your money, I will have Rs.75/-  How much money did John have ?
a. 45
b. 60
c. 48
d. 37.5
Ans: B
Explanation: Let the money with Mark and John are M and J respectively.
Now
M + J/2 = 75
M/3 + J = 75
Solving we get M = 45, and J = 60.

11. Eesha has a wheat business.  She purchases wheat from a local wholesaler of a particular cost per pound.  The price of the wheat of her stores is $3 per kg. Her faulty spring balance reads 0.9 kg for a KG. Also in the festival season, she gives a 10% discount on the wheat. She found that she made neither a profit nor a loss in the festival season. At what price did Eesha purchase the wheat from the wholesaler ? a. 3 b. 2.5 c. 2.43 d. 2.7 Ans: C Explanation: Faulty spring balance reads 0.9 kg for a kg" means that she sells 1 kg for the price of 0.9 kgs, so she looses 10% of the price because of the faulty spring balance. She looses another 10% because of the discount. So, she actually sells 1 kg for$3×0.9×0.9=$2.43 and since at that price she made neither a profit nor a loss, then Eesha purchase the wheat from the wholesaler for$2.43.

12. Raj goes to market to buy oranges.  If he can bargain and reduce the price per orange by Rs.2, he can buy 30 oranges instead of 20 oranges with the money he has.  How much money does he have ?
a. Rs.100
b. Rs.50
c. Rs.150
d. Rs.120
Ans: D
Explanation: Let the money with Raj is M.  So M20M30=2.  Check options.  Option D satisfies.

13. A city in the US has a basketball league with three basketball teams, the Aziecs, the Braves and the Celtics.  A sports writer notices that the tallest player of the Aziecs is shorter than the shortest player of the Braves.  The shortest of the Celtics is shorter than the shortest of the Aziecs, while the tallest of the Braves is shorter than the tallest of the Celtics.  The tallest of the Braves is taller than the tallest of the Aziecs.
Which of the following can be judged with certainty ?

X) Paul, a Brave is taller than David, an Aziec
Y) David, a Celtic, is shorter than Edward, an Aziec

a. Both X and Y
b. X only
c. Y only
d. Neither X nor Y
Ans: B
Sol: We solve this problem by taking numbers. Let the shortest of Braves is 4 feet.  Then tallest of Aziecs is less than 4. So let it be 3 feet.
A ->  2 - 3
B -> 4 - 6
C -> 1 - 7
From the above we can safely conclude X is correct. but Y cannot be determined.

14. There are 3 classes having 20, 24 and 30 students respectively having average marks in
an examination as 20,25 and 30 respectively.  The three classes are represented by A, B and C and you have the following information about the three classes.
a. In class A highest score is 22 and lowest score is 18
b. In class B highest score is 31 and lowest score is 23
c. In class C highest score is 33 and lowest score is 26.

If five students are transferred from A to B, what can be said about the average score of A; and what will happen to the average score of C in a transfer of 5 students from B to C ?
a. definite decrease in both cases
b. can't be determined in both cases
c. definite increase in both cases
d. will remain constant in both cases
Ans: B
Explanation:
Class A average is 20. And their range is 18 to 22
Class B average is 25. And their range is 23 to 31
Class A average is 30. And their range is 26 to 33
If 5 students transferred from A to B, A's average cannot be determined but B's average comes down as the highest score of A is less than lowest score of B.
If 5 students transferred from B to C, C's average cannot be determined the B's range fo marks and C's range of  marks are overlapping.

15. The value of a scooter depreciates in such a way that its value of the end of each year is 3/4 of its value of the beginning of the same year.  If the initial value of the scooter is Rs.40,000, what is the value at the end of 3 years ?
a. Rs.13435
b. Rs.23125
c. Rs.19000
d. Rs.16875
Ans: D
Explanation: 40,000(34)3=16875

16. Rajiv can do a piece of work in 10 days , Venky in 12 days and Ravi in 15 days.  They all start the work together, but Rajiv leaves after 2 days and Venky leaves 3 days before the work is completed.  In how many days is the work completed ?
a. 5
b. 6
c. 9
d. 7
Ans: D
Explanation: Let the work be 60 units. If venky leave 3 days before the work, Last 3 days must be worked by Ravi. So the remaining days of work be x days, total days to complete the work be x + 3 days.
Now Capacities of Rajiv is 60/10 = 6, Venky is 5, Ravi is 4.
(6 + 5 + 4) 2 + (5 + 4) (x – 3) + 4 x 3 = 60.
30 + 9x – 27 + 12 = 60
9x – 15 =30
9x = 45
x = 5
So total days to complete the work = 2 + 5 = 7 days.

17. A man has a job, which requires him to work 8 straight days and rest on the ninth day.  If he started work on Monday, find the day of the week on which he gets his 12th rest day.
a. Thursday
b. Wednesday
c. Tuesday
d. Friday
Ans: B
Explanation:
He works for 8 days and takes rest on the 9th day. So On the 12th rest day, there are 9 x 12 = 108 days passed. Number of odd days = (108 - 1) / 7 = 107 / 7 = 2. So the 12th rest day is wednesday.

18. On a 26 question test, five points were deducted for each wrong answer and eight points were added for each correct answer.  If all the questions were answered, how many were correct, if the score was zero ?
a. 10
b. 12
c. 11
d. 13
Ans: A
Explanation:
Take options and check. If 10 are correct, his score is 10 x 8 = 80.  But 16 are wrong. So total negative marking is 16 x 5 = 80. So final score is zero.

### Polaris – Aptitude & Reasoning

1. Fill in the blank to complete the series CMM, EOO, CQQ,____?
(a) ISS                   (b) KUU                                (c) YUT                  (d) RED
Ans: (a)
1. What was the day on 17th June 1998?
(a) Monday                        (b) Tuesday                        (c) Thursday                       (d) Wednesday
Ans: (d)
The Number of odd days are arrived at as under:
Between 1600 and 1900 the number of odd days is —————–1
In 1998 completed years 97and of this Number of leap years are 24 and ordinary years 73
Total number of odd days in 97 years -> (24×2)+(73×1)-> 121 days.
From 1.1.1998 to 17.06.98 the number of odd days are {3+3+2+3+3(17-two completed weeks)]
Thus the total number of odd days are—– 1 + 121 + 14 = 136 -> completed weeks -> 19
and remaining odd days -> 3 ie Wednesday.
1. A 6% stock yield 8%, the market value of stock is?
(a) 48                     (b) 75                    (c) 96                     (d) 133.33
Ans: (b)
The yield of 6% is on a stock value of Rs 100.00
The point to note here is if the yield increases then the stock value decreases and vice versa.
Hence the market value is ->  100 x 6/8 -> Rs 75.00
1. A long rope to be cut ,to make 23 small pieces if it double folded to start with how many times it need to be cut?
(a) 9                       (b) 23                    (c) 11                     (d) 12
Ans: (c)
The rope is double folded. Hence each cut will give two small pieces. Thus 11 cuts
will give 22 pieces and the last remaining folded portion will be the 23 piece.
1. What fits in the blank of the following sequence?
Amble,   ______       jog,       run
(a) walk                                (b) creep             (c) sprint              (d) crawl
Ans: (a)
1. Find the largest factor of 2520 that is not divisible by 6?
(a) 315               (b) 225                  (c) 325                   (d) 215
Ans: (a)
1. Find the greatest number that divides 364,  414 and 539 with same remainder in each case?
(a) 25                  (b) 35                    (c) 45                     (d) 55
Ans: (a)
1. N is the 5 digit number 8A65B in which A and B are digit and N is divisible by 24.
What is the smallest number  N can be?
(a) 82653                           (b) 81656             (c) 82656              (d) 80654
Ans: (c)
The divisor 24 is a multiple of 4 and the rule of divisibility for 4 is the last two digits divisible by 4.
Only (b) and (c) fulfills this condition  and of this (c) is the number perfectly divisible by 24.
1. A number is increased consecutively two times by 20% each the original number is actually increased by?
(a) 40%              (b) 42%                 (c) 44%                 (d) 20%
Ans: (c)
Successive change in percentage is given by the formula — X + Y + XY/100
where X and Y are the successive changes in percentages.
Applying this we get ->  20 + 20 + 400/100 -> 44%
1. If ‘a is divided by b’ the result is 3/4 ,If ‘b is divided by c’ the result is 5/6 then the result when ‘a is divided by c’?
(a) 1/8                (b) 7/8                  (c) 5/8                   (d) 3/8
Ans: (c)
A/B = ¾ _> 4A = 3B
B/C = 5/6 -> 6B = 5C -> 8A = 5C  (Note 3B = 4A)
Hence A/C = 5/8
1. Optimist is to cheerful as pessimist is to
(a) gloomy                        (b) mean                             (c) petty               (d) helpful
Ans: (a)
1. Chiyo is younger than Pimpkin , Sayri is older than Pimpkin, who is younger than Chiyo?
(a) Sayri                             (b) pimkin           (c) can’t be determined                     (d)No one
Ans: (d)
1. In a certain code AUDIT is written as 2*67$and PUB is written as 8*5 how is BUT written that code? (a)$56                        (b) 5*$(c)$57             (d) 6*\$                  (e) none of these
Ans: (b)
1. Seven eighth of number added to 72 doubles the number read Soren “Is this a joke?” Larry looked at the paper and said “No it is the number of my locker” what is the number?
(a) 68                                 (b) 78                    (c) 64                     (d) 74
Ans: (c)
Let the Number be N. Then we have an equation -> 7N/8 + 72 = 2N
Solving, we get value of N as 64.
1. A jar contains number of pennies, the pennies can be divided into equal share among 3, 4,5,6,7 or 8 child left with number of pennies, what is the least number of pennies that the jar contains?
(a) 440                             (b) 840                  (c) 940                  (d) 640
Ans: (b) (Find the LCM of all the numbers)
1. The day that dawn three days after tomorrow is Friday what day of the week dawned two day before yesterday?
(a) Saturday                  (b) Sunday          (c) Wednesday                 (d) Friday
Ans: (d)   Three days after tomorrow is Friday. So, tomorrow is Tuesday and today is Monday.
Yesterday was Sunday and two days prior to yesterday was again Friday.
1. A number is greater than 10 has the property that when divided either by 5 or 7 the remainder is 1,what is the smallest odd counting number that have?
(a) 61                                (b) 51                    (c) 71                     (d) 81
Ans: (c) LCM of 5 and 7 is 35 and among the choice only 71 will leave a reminder of 1 when divided by 35.
1. Three digit number 104 has a digit sum of 1+0+4 (or) 5 how many different three digit number, including 104 each have digit sum of 5?
(a) 35                               (b) 25                    (c) 15                     (d) 43
Ans: (c)
The Nos are: 104, 113, 122, 131, 140, 203, 212, 221, 230, 302, 311, 320, 401, 410, 500
1. In certain code ‘RANGE’ coded 12345 and ‘RANDOM’ is coded as 123678 then the code of ‘MANGO’ is
(a)  82543                        (b) 82347             (c) 84563              (d) 82357
Ans: (b)
1. Find the odd one out 8, 27, 64, 100, 125, 216, 343
(a) 27                                (b) 100                  (c) 125                   (d) 343
Ans: (b)
all the others are perfect cube values.