CMC
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Analytical Reasoning
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(15) steps problem
There are six steps that lead from the first to the second floor.
No two people can be on the same step.
Mr A is two steps below Mr C
Mr B is a step next to Mr D
Only one step is vacant ( No one standing on that step )
Denote the first step by step 1 and second step by step 2 etc.
(1) If Mr A is on the first step, Which of the following is true?
(A) Mr B is on the second step
(B) Mr C is on the fourth step.
(C) A person Mr E, could be on the third step
(D) Mr D is on heigher step than Mr C.
Ans : (D)
(2). If Mr E was on the third step & Mr B was on a higher step than
Mr E which step must be vacant
(A) step 1 (B) step 2 (C) step 4 (D) step 5 (E) step 6
Ans : (A)
(3). If Mr B was on step 1, which step could A be on?
(A) 2&e only (B) 3&5 only (C) 3&4 only (D) 4&5 only (E) 2&4 only
Ans : (C)
(4). If there were two steps between the step that A was standing and the
step that B was standing on, and A was on a higher step than D , A
must be on step
(A) 2 (B) 3 (C) 4 (D) 5 (E) 6 Ans: (C)
(5). Which of the following is false
i. B&D can be both on oddnumbered steps in one configuration
ii. In a particular configuration A and C must either both
an odd numbered steps or both an evennumbered steps
iii. A person E can be on a step next to the vacant step.
(A) i only (B) ii only (C) iii only Ans : (C)
Swimmers problem (6 – 9 )
Six swimmers A B C D E F compete in a race. There are no
ties. The out comes are as follows.
1. B does not win.
2. Only two swimmers seperate E & D
3. A is behind D & E
4. B is ahead of E , wiht one swimmer intervening
5. F is a head of D
(6). who is fifth
(A) A (B) B (C) C (D) D (E) E Ans : (E)
(7) How many swimmers seperate A and F “
( A) 1 (B) 2 (C) 3 (D) 4 (E) not deteraminable from the given info.
Ans 🙁 D )
(8). The swimmer between C & E is
(A) none (B) F (C) D (D) B (E) A Ans : (A)
(9). If the end of the race, swimmer D is disqualified by the Judges
then swimmer B finishes in which place
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5 Ans : (B).
Cimney problem ( 10 – 14 )
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Five houses lettered A,B,C,D, & E are built in a row next to each
other. The houses are lined up in the order A,B,C,D, & E. Each of the
five houses has a coloured chimney. The roof and chimney of each house
must be painted as follows.
1. The roof must be painted either green,red ,or yellow.
2. The chimney must be painted either white, black, or red.
3. No house may have the same color chimney as the color of roof.
4. No house may use any of the same colors that the every next house
uses.
5. House E has a green roof.
6. House B has a red roof and a black chimney
10). Which of the following is true ?
(A) At least two houses have black chimney.
(B) At least two houses have red roofs.
(C) At least two houses have white chimneys
(D) At least two houses have green roofs
(E) At least two houses have yellow roofs
Ans: (C)
11). Which must be false ?
(A) House A has a yellow roof
(B) House A & C have different colour chimney
(C) House D has a black chimney
(D) House E has a white chmney
(E) House B&D have the same color roof.
Ans: (B)
12). If house C has a yellow roof. Which must be true.
(A) House E has a white chimney
(B) House E has a balck chimney
(C) House E has a red chimney
(D) House D has a red chimney
(E) House C has a balck chimney
Ans: (A)
13). Which possible combinations of roof & chimney can house
I. A red roof 7 a black chimney
II. A yellow roof & a red chimney
III. A yellow roof & a black chimney
(A) I only (B) II only (C) III only (D) I & II only (E) I&II&III
Ans; (E)
14). What is the maximum total number of green roofs for houses
Ans: (C)
15). There are 5 red shoes, 4 green shoes. If one drasw randomly a shoe
what is the probability of getting redshoe is 5c1/9c1
16). What is the selling price of a car? cost of car is Rs 60 &
profit 10% profit over selling price Ans : Rs 66/
17). 1/3 of girls , 1/2 of boys go to canteen .What factor and total
number of clasmates go to canteen. Ans: cannot be determined.
18). price of a product is reduced by 30% . What percentage should
be increased to make it 100% Ans: 42.857%
19) There is a square of side 6cm . A circle is inscribed inside the
square. Find the ratio of the area of circle to square.
r=3
circle/square = 11/14
20). Two candles of equal lengths and of different thickness are there.
The thicker one will last of six hours. The thinner 2 hours less
than the thicker one.
Ramesh light the two candles at the same time. When he went to bed
he saw the thicker one is twice the length of the thinner one. For
how long did Ramesh lit two candles .
Ans: 3 hours.
21). M/N = 6/5 3M+2N = ? Ans: cannot be determined
22). p/q = 5/4 2p+q= ? cannot determined.
23). If PQRST is a parallelogram what it the ratio of triangle PQS &
parallelogram PQRST
Ans: 1:2
24). cost of an item is Rs 12.60 7 profit is 10% over selling price
what is the selling price
Ans: Rs 13.86/
25). There are 6 red shoes & 4 green shoes . If two of red shoes are
drawn what is the probability of getting red shoes
Ans: 6c2/10c2
26). 15 lts of water containing 20% alcohol, then added 5 lts of water.
What is % alcohol.
Ans : 15%
27). A worker pay 20/ day , he works 1, 1/3,2/3,1/8.3/4 in a week.
what is the total amount paid for that worker
Ans : 57.50
28). The value of x is between 0 & 1 which is the larger?
A) x B) x^2 C) x D) 1/x
Ans : (D)
DATA SUFFICIENCY
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(A) (1) alone sufficient
(B) (2) alone sufficient
(C) both together are sufficient
(D) (1) alone & (2) alone sufficient
(E) information not sufficient
1). A man of 6 feet tall is standing near a light on the top of a pole.
what is the length of the shadow cost by the man.
(1) The pole is 18 feet high
(2) The man is 12 feet high Ans: (C)
2). Two pipes A and B empty into a resrvoir , pipe A can fill the reservoir
in 30 minutes by itself. How long it will take for pipe A and pipe B
together to fill up the reservoir.
(1) By itself, pipe B can fill up the reservoir in 20 minutes
(2) pipe B has a larger crosssectional area than pipe A
Ans: (A)
3). K is an integer. Is K is divisible by 12
(1) K is divisible by 4
(2) K is divisible by 3 Ans: (C)
4). How far it from A to B
(1) It is 15 miles from A to C
(2) it is 25 miles from C to B Ans: (E)
5). Was Melissa Brown’s novel published?
(1). If Melissa Brown’s novel was published she would receive
atleast $1000 in royalities during 1978
(2). Melissa Brown’s income for 1978 was over $1000
Ans: (E)
6). Does every bird fly?
(1) Tigers do not fly.
(2) Ostriches do not fly
Ans: (B)
7). How much does John weigh? Jim weigh 200 pounds.
(1) Toms weight plus Moes weight equal to John’s weight.
(2) John’s weight plus Moe’s weight equal to Twice Tom’s weight.
Ans: (C)
8). Is the figure ABCD is a rectangle
A —————— B
 
 
 
 
D —————— C
(1). x=90(degrees)
(2). AB=CD
Ans: (E)
9). Find x+2y
(1). x+y=10
(2). 2x+4y=20
Ans: (B).
10). Is angle BAC is a right angle 
y

x z
——
(1). x=2y
(2) y=1.5z
Ans: (E)
11). Is x greater than y
(1) x=2k
(2) k=2y Ans: (E)
12). A piece of string 6 feet long is cut into three smaller pieces. How
long is the longer of ther three pieces?
(1). Two pieces are the same length.
(2) One piece is 3 feet 2 inches lone
Ans: (B)
13). How many rolls of wall paper necessary to cover the walls of a
room whose floor and ceiling are rectangles 12 feet wide and
15 feet long
(1). A roll of paper covers 20 sq feet
(2). There are no windows in the walls
Ans : (E)
14). x and y are integers that are both less than 10. Is x>y?
(1). x is a multiple of 3
(2). y is a multiple of 2
Ans: (E).
15). Fifty students have signed up for atleast one of the courses
GERMANI 1 & ENGLISH 1, how many of the 50 students are taking
GERMANI 1 but not ENGLISH 1.?
(1). 16 students are taking GERMANI 1 & ENGLISH 1
(2). The number of students taking ENGLISH 1 but not GERMANI 1 is
the same as the number of students taking GERMANI 1.
Ans: (C)
16). Is ABCD is a square ? A ———— B
(1). AD = AB x 
(2). x=90(degres)  
 
D ———— C
Ans: (E).
17). How much card board will it take to make a rectangular bos with
a lid whose base has length 7 inches.
(1). The width of the box 5 inches
(2). The height of the box will be 4 inches
Ans: (C).
18). Did ABC company made profit in 1980?
(1). ABC company made a profit in 1979.
(2). ABC company made a profit in 1981.
Ans: (E).
19). How much is Janes salary?
(1). Janes salary is 70% of John’s salary
(2). Johns salary is 50% of Mary’s salary
Ans: (E).
20). Is x>1
(1) x+y=2
(2) y<0 Ans: (c)
21). How many of the numbers x and y are positive? Both
x and y are less than 20
(1) x is less than 5
(2) x+y =24
Ans: (B)
22). Is the angle ACB is right angle A
(1). y=z 
(2). (AC)^2+CB^2=AB^2  z



x y
C ——– B
Ans: (B).
23). How far it from town A to town B? Town C is 12 miles east of
town A
(1). Town C is south of town B
(2). It is 9 miles from town B to town C
Ans :(C)
24). A rectangular field is 40 yards long. Find the area of the field.
(1). A fence around the boundary of the field is 140 yards long
(2). The field is more than 20 yards width
Ans: (A).
25). An industrial plant produces bottles. In 1961 the number
of bottles produced by the plant was twice the number of
produced in 1960. How many bottles were produced altogether
in the year 1960, 61,&62
(1). In 1962 the number of bottles produced was 3 times the
number of produced in 1980
(2). In 1963 the number of bottles produced was one half the
total produced in the years 1960,1961,1962.
Ans: (E).
26). Is xy > 1 ? x & y are both positive
(1) x is less than 1
(2) y is greater than 1
Ans : (E)
27). Is it a Rambus ———
(1). All four sides are equal / /
(2) Total internal angle is / /
360 / /
———
Ans: (E)
28). How many books are in the book shelf
(1) The book shelf is 12 feet long
(2). The average weight of each book is 1.2 pound
Ans: (E).
29). What is the area of circle?
(1). Radius r is given
(2). Perimeter is 3 times the area
Ans: (A).
ARITHMATIC
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1). Total distance is 120 km . Going by 60kmph and coming back by
40kmph what is the average speed? Ans: 48kmph
2). A school have 30% from MAHARASTRA .Out of this 20% from
BOMBAY students. Find the total percentage of BOMBAY
Ans: 6%
3). An equilateral triangle of side 3 inch is given. How many
equilateral triangles of side 1 inch can be formed from it
Ans : 9
4). A/B = 3/5 15A = ?
Ans : 9B
5). Each side of a rectangle is increased by 100% .
How much the percentage of area will be increased
Ans : 300%
6). Perimeter of the back whell = 9 feet, front wheel = 7 feet
on a certain distance the front wheel gets 10 revolutions
more than back wheel . what is the distance?
Ans : 315 feet.
7). Perimeter of front wheel =30, back wheel = 20. If front wheel
revolves 240 times. Howm many revolutions will the back wheel
take? Ans: 360 times
8). 205 of 6 liter solution and 60% of 4 liter solution is mixed
What percentage of the mixture of solution
Ans: 36%
9). City A population is 68000, decreasing at a rate of 80 per year
City B having population 42000 increasing at a rate of 120 per
year. In how many years both the cities will have same
population
Ans: 130 years
10). Two cars, 15 km apart one is turning at a speed of 50kmph
other at 40kmph . How will it take to two cars meet.
Ans 3/2 hours
11). A person wants to buy 3 paise and 5 paise stamps costing exactly
one rupee. If he buys which of the following number of stamps.
he wont able to buy 3 paise stamps
Ans: 9
12). There are 12 boys and 15 girls, How many different dancing
groups can be formed.
Ans: 180
13). Which of the following fractions is less than 1/3
(1) 22/62 (2) 15/46
Ans: 15/46
14). Two circles , one circle is inscribed and another circle is
outscribed over a square. What is the ratio of area of inner
to outer circle.
Ans: 1 : 2
Plumber problem ( 15 – 17)
Miss Dean wnats to renovate her house. She hires a plumber,
a carpenter, a painter an electricial and interior deorator.
The work to be finished in one working (Monday – Friday ).
Each worker will take the full day to do his job. Miss Dean
permit only one person to work each day.
I. The painter cna work only after the plumber and the
carpenter have finished their jobs
II. The interior decorator must do his job before the
electrician.
III. The carpenter cannot work on Monday or Tuesday
15) If the painter work on Thursday, which one of the following
alternatives is possible?
(A) The electrician works on Tuesday.
(B). The electrician works on Friday.
(C) The interior decorator works after the painter does.
(D). The painter works on consecutive days
(E). Miss Dean cannot fit all of the workers int schedule
Ans: (B).
16). If the painter works on Friday which of the following must be false?
(A) . The carpenter may works on Wednesday
(B). The carpenter and the electrician may work on
consecutive days
(C). If the carpenter works on Thursday, the electrician has
to work on wednesday
(D). The plumber may work before the electrician does
(E). The electrician may work on Tuesday
Ans: (C).
17). Which argument is possible?
(A). The electrician will works on Tuesday and the interior
decorator on Friday
(B). The painter will work on wednesday and plumber on thursday
(C). The carpenter will works on Tuesday and the painter on Friday
(D). THe painter will work on Monday and the carpenter on Thursday
(E). The carpenter will work on Wednesday and the plumber on Thursday
Ans: (E).
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There is one section Figures , like 4 figures are given and we
have to find the next one. In this 10 question are given
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In IITKGP he didn’t keep the Test
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