Amcat 2

USEFUL FOR ENGINEERING STUDENTS PREPARING FOR APTITUDE

1. AMCAT 2

2. AMCAT QUANTITATIVE ABILITY
BASIC
NUMBERS
•Decimals & Fractions Basic Algebra
•Factorization Divisibility
•HCF & LCM
WORD
PROBLEMS
•Application of algebra to real worldCommon Applications
•Direct and Inverse Proportion Speed–time–distance
•Profit/LossPercentage Age Relations Mixtures
Probability
•Permutation & CombinationFactorial Notation
•Principles of counting P&C with repetition, restriction & counting
•Probability Addition, Multiplication Law, Events Dependent, Independent, exclusive events
Power
•Fractional and Negative powersGraphical, Intuitive, Understanding
•Logarithm/antilog definition and properties Word ProblemsMixed with Algebra

3. DECIMALS & FRACTIONS
•892.7 -573.07 -95.007 =?
•i) 224.623 ii) 224.777iii) 233.523 iv)414.637
•Choice 1.

4. FRACTIONS

5. FRACTIONS

6. DIVISIBILITY
•What least number be added to 5200 to get a
number exactly divisible by 180?
(1) 160 (2) 60 (3) 20 (4) 180
•180 = 5 X 4 X 9.
•5200 –160 = 5040 DIVISIBLE BY 9,4,5.
•5200 –60 = 5140 NOT DIVISIBLE BY 9
•5200 –20 = 5080 NOT DIVISIBLE BY 9
•5200 –180 NOT DIVISIBLE BY 9.

7. DIVISIBILITY
•A number when divided by 32 leaves the
remainder 29. This number when divided by 8
will leave the remainder (1) 3 (2) 5 (3) 7 (4) 29
•Let the number be 32k + 29.
•32k + 29 = 32k + 24 + 5
•8(4k+3) + 5.
•The remainder is 5.

8. HCF & LCM

9. HCF & LCM
•Four different electronic devices make a beep after every 30
minutes, 1 hour, 3/2 hour and 1 hour 45minutes respectively.
•All the devices beeped together at 12 noon.
•They will again beep together at:
•i) 12 Midnight ii) 3 a.miii) 6 a.m. iv) 9 a.m
Interval after which the devices will beep together
= (L.C.M. of 30, 60, 90, 105) min.
= 1260 min.
= 21 hrs.
So, the devices will again beep together 21 hrs. after 12 noon i.e., at 9 a.m.

10. HCF & LCM

11. DIRECT & INVERSE PROPORTION

12. TIME,SPEED AND DISTANCE

13. PROFIT & LOSS
-5 x = -1000 X = 200

14. PERCENTAGE
•The difference between a discount of 35% and
two successive discounts of 20% and 20% on a
certain bill was Rs. 22. Find the amount of the
bill.
(1) Rs. 1100 (2) Rs. 200 (3) Rs. 2200 (4) Data
inadequate
•Successive 20% discount means 36% discount.
•The difference between 35% and 36% is 1%.
•1% = 22 means the answer is 2200.

15. AGE
•The average age of A and B is 20 years. If C
were to replace A, the average would be 19
and if C were to replace B, the average would
be 21. What are the ages of A, B and C?
(1) 22, 18, 20 (2) 18, 22, 20
(3) 22, 20, 18 (4) 18, 20, 22

16. MIXTURES
•Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a
third variety in the ratio 1:1:2.
•If the mixture is worth Rs. 153 per kg, the price of the third
variety per kg will be:
•i) Rs. 169.50 ii) Rs. 170 iii) Rs. 175.50iv) Rs. 180

17. Since first and second varieties are mixed in equal proportions.
So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg
and the other at say, Rs. xper kg in the ratio 2 : 2, i.e.,1 : 1. We have to
find x.
By the rule of alligation, we have:
So, their average price = Rs.
126 + 135
= Rs. 130.50
2
Costof 1 kg of 1
st
kind MeanPrice Cost of 1 kg of 2
nd
kind
130.50 153 X
X–153 22.50
x-153
= 1
22.50
x-153 = 22.50
x= 175.50

18. PERMUTATION & COMBINATION
•In how many different ways can the letters of the word 'LEADING'
be arranged in such a way that the vowels always come together?
•A. 360B. 480C. 720D. 5040
•E. None of these
•The word 'LEADING' has 7 different letters.
•When the vowels EAI are always together, they can be supposed to
form one letter.
•Then, we have to arrange the letters LNDG (EAI).
•Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways.
•The vowels (EAI) can be arranged among themselves in 3! = 6 ways.
•Required number of ways = (120 x 6) = 720.

19. FACTORIAL NOTATION
•What is the highest power of 5 that divides 90 x 80 x
70 x 60 x 50 x 40 x 30 x 20 x 10?
•i) 10 ii) 12 iii) 14 iv) None of these
•We should find out the highest power of 5 that
divides 9! X 10
9
= 9! X 5
9
x 2
9
.
•The highest power of 5 which divides 9! Is 1.
•Hence the answer is 10.

20. PRINCIPLES OF COUNTING

21. PERMUTATION & COMBINATION
WITH RESTRICTIONS
•In a group of 6 boys and 4 girls, four children are to be selected. In how
many different ways can they be selected such that at least one boy
should be there?
•A. 159 B. 194 C. 205 D. 209
•E. None of these
•We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1
girl) or (4 boys).
•Required number of ways
= (
6
C
1x
4
C
3) + (
6
C
2x
4
C
2) + (
6
C
3x
4
C
1) + (
6
C
4)
= (
6
C
1x
4
C
1) + (
6
C
2x
4
C
2) + (
6
C
3x
4
C
1) + (
6
C
2)
= (24 + 90 + 80 + 15)
= 209.

22. PERMUTATIONS

23. •How many 3-digit numbers can be formed from the digits
2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the
digits is repeated?
•A. 5 B. 10C. 15D. 20
Since each desired number is divisible by 5, so we must have 5
at the unit place. So, there is 1 way of doing it.
The tens place can now be filled by any of the remaining 5
digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens
place.
The hundreds place can now be filled by any of the remaining
4 digits. So, there are 4 ways of filling it.
Required number of numbers = (1 x 5 x 4) = 20.

24. FRACTIONAL POWERS

25. NEGATIVE POWERS
•What is the value of 0
-10
?
•i) 0 ii) 1 iii) -10 iv) None of these
•0.

26. •25
25
is divided by 24, the remainder is
•1) 23 2) 22 3) 1 4) 2
•25
25
= (24 + 1)
25
= 24K + 1.
•CHOICE 3.

27. •Consider the following statements: If a sum of money is
lent at simple interest, then the
•1. Money gets doubled in 5 years if the rate of interest is
50/3 %.
•2. Money gets doubled in 5 years if the rate of interest is
20%.
•3. Money becomes four times in 10 years if it gets doubled
in 5 years.
•Of these Statements:
•i) 1 and 3 are correct ii) 2 alone is correct iii) 3 alone is
correct iv) 2 and 3 are correct
•2 alone is correct.

29. •The unit digit in the expression
•( 36
234
x 33
512
x 39
180
) –(54
29
x 25
123
x 31
512
)
will be
•(a) 2 (b) 6 (c) 8 (d) 4

30. ATTENTION TO DETAIL
•Follow the directions given below to answer the questions that follow.
Your answer for each question below would be:
•A.If all the THREE items given in the question are exactly ALIKE
•B.If only the FIRST and SECOND items are exactly ALIKE.
•C.If only the FIRST and THIRD items are exactly ALIKE.
•D.If none of the above
•
•49A0067DF667016A0067DF667016A0067DF667106
• (a) A (b) B (c) C (d) D
•
•50Janmasthami Janmasthhami Jamnasthami
• (a) A (b) B (c) C (d) D
•

31. •If * stands for +, + stands for -, and -stands for /, then 27/5*8+11-7=?
•(a) 141.4(b)38.4 (c) 16.4 (d)36.1
•
•If * stands for -, / stands for +, + stands for / and –stands for *, then which
of the following is TRUE?
•A)8/12*4+20-8=18.4 B)12*8/4+20-8= -5.6 C)8*4/12+8-8= -12.2
D)8*8/4+20-8= -4
•(a) A (b) B (c) C (d) D
•
•Identify the correct match 345611242627
•A) 345612414627 B) 345611426227 C)345611624227 D) 345616242227
• (a) A (b) B (c) C (d) D