USEFUL FOR ENGINEERING STUDENTS PREPARING FOR APTITUDE

1. AMCAT 2

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

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

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.m iii) 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, their average price = Rs.
126 + 135
2
= Rs. 130.50
So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg
and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to
find x.
By the rule of alligation, we have:
Cost of 1 kg of 1st kind
Mean Price
Cost of 1 kg of 2nd kind
130.50
153
X
X–153
22.50
x - 153
22.50
=1
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. 360
B.
480
C.
720
D.
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 109 = 9! X 59 x 29.
• 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
= (6C1 x 4C3) + (6C2 x 4C2) + (6C3 x 4C1) + (6C4)
= (6C1 x 4C1) + (6C2 x 4C2) + (6C3 x 4C1) + (6C2)
= (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.
10
C.
15
D.
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
• 0.
ii) 1
iii) -10
iv) None of these

26. •
•
•
•
2525 is divided by 24, the remainder is
1) 23
2) 22
3) 1
4) 2
2525 = (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
• ( 36234 x 33512 x 39180) – (5429 x 25123 x 31512)
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
•
• 49 A0067DF667016 A0067DF667016 A0067DF667106
•
(a) A
(b) B
(c) C
(d) D
•
• 50 Janmasthami
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