ssc math model set paper

1. The average wages of a worker during a fortnight
comprising 15 consecutive working days was Rs.90 per
day. During the first 7 days, his average wages was Rs.87/
day and the average wages during the last 7 days was
Rs.92 /day. What was his wage on the 8th day?
1. 83
2. 92
3. 90
4. 97
Ans : D
2. The average of 5 quantities is 6. The average of 3 of
them is 8. What is the average of the remaining two
numbers?
1. 6.5
2. 4
3. 3
4. 3.5
Ans : C
3. The average temperature on Wednesday, Thursday and
Friday was 250. The average temperature on Thursday,
Friday and Saturday was 240. If the temperature on
Saturday was 270, what was the temperature on
Wednesday?
1. 240
2. 210
3. 270
4. 300
Ans : D
4. The average age of a group of 12 students is 20years.
If 4 more students join the group, the average age
increases by 1 year. The average age of the new students
is
1. 24
2. 26
3. 23
4. 22
Ans : A
5. When a student weighing 45 kgs left a class, the
average weight of the remaining 59 students increased
by 200g. What is the average weight of the remaining 59
students?
1. 57 kgs
2. 56.8 kgs
3. 58.2 kgs
4. 52.2 kgs
Ans : A
6. Three math classes: X, Y, and Z, take an algebra test.
The average score in class X is 83.
The average score in class Y is 76.
The average score in class Z is 85.
The average score of all students in classes X and Y
together is 79.
The average score of all students in classes Y and Z
together is 81.
What is the average for all the three classes?
1. 81
2. 81.5
3. 82
4. 84.5
Ans : B
7. The average weight of a class of 24 students is 36
years. When the weight of the teacher is also included,
the average weight increases by 1kg. What is the weight
of the teacher?
1. 60 kgs
2. 61 kgs
3. 37 kgs
4. None of these
Ans : B
8. The average of 5 quantities is 10 and the average of 3
of them is 9. What is the average of the remaining 2?
1. 11
2. 12
3. 11.5
4. 12.5
Ans : C
9. The average age of a family of 5 members is 20 years.
If the age of the youngest member be 10 years then what
was the average age of the family at the time of the birth
of the youngest member?
1. 13.5
2. 14
3. 15
4. 12.5
Ans : D
10. A student finds the average of 10 positive integers.
Each integer contains two digits. By mistake, the boy
interchanges the digits of one number say ba for ab. Due
to this, the average becomes 1.8 less than the previous
one. What was the difference of the two digits a and b?
1. 8
2. 6
3. 2
4. 4
Ans : C
11. Average cost of 5 apples and 4 mangoes is Rs. 36. The
average cost of 7 apples and 8 mangoes is Rs. 48. Find
the total cost of 24 apples and 24 mangoes.
1. 1044
2. 2088
3. 720
4. 324
Ans : B
Interest
1. A father left a will of Rs.35 lakhs between his two
daughters aged 8.5 and 16 such that they may get equal
amounts when each of them reach the age of 21 years.
The original amount of Rs.35 lakhs has been instructed to
be invested at 10% p.a. simple interest. How much did the
elder daughter get at the time of the will?
1. Rs. 17.5 lakhs
2. Rs. 21 lakhs
3. Rs. 15 lakhs
4. Rs. 20 lakhs
Ans : B
2. What will Rs.1500 amount to in three years if it is
invested in 20% p.a. compound interest, interest being
compounded annually?
1. 2400
2. 2592
3. 2678
4. 2540
Ans : B
3. If a sum of money grows to 144/121 times when
invested for two years in a scheme where interest is
compounded annually, how long will the same sum of
money take to treble if invested at the same rate of
interest in a scheme where interest is computed using
simple interest method?
1. 9 years
2. 22 years
3. 18 years
4. 33 years
Ans : B
4. The population of a town was 3600 three years back. It
is 4800 right now. What will be the population three years
down the line, if the rate of growth of population has been
constant over the years and has been compounding
annually?
1. 6000
2. 6400
3. 7200
4. 9600
Ans : B
5. A man invests Rs.5000 for 3 years at 5% p.a. compound
interest reckoned yearly. Income tax at the rate of 20%
on the interest earned is deducted at the end of each
year. Find the amount at the end of the third year.
1. 5624.32
2. 5630.50
3. 5788.125
4. 5627.20
Ans : A
6. The difference between the compound interest and the
simple interest on a certain sum at 12% p.a. for two years
is Rs.90. What will be the value of the amount at the end
of 3 years?
1. 9000
2. 6250
3. 8530.80
4. 8780.80
Ans : D
7. Vijay invested Rs.50,000 partly at 10% and partly at
15%. His total income after a year was Rs.7000. How
much did heinvest at the rate of 10%?
1. Rs.40,000
2. Rs.40,000
3. Rs.12,000
4. Rs.20,000
Ans : B
8. A sum of money invested for a certain number of years
at 8% p.a. simple interest grows to Rs.180. The same sum
of money invested for the same number of years at 4%
p.a. simple interest grows to Rs.120 only. For how many
years was the sum invested?
1. 25 years
2. 40 years
3. 33 years and 4 months
4. Cannot be determined
Ans : A
9. How long will it take for a sum of money to grow from
Rs.1250 to Rs.10,000, if it is invested at 12.5% p.a simple
interest?
1. 8 years
2. 64 years
3. 72 years
4. 56 years
Ans : D
10. Rs. 5887 is divided between Shyam and Ram, such that
Shyamâ €™s share at the end of 9 years is equal to Ramâ
€™s share at the end of 11 years, compounded annually at
the rate of 5%. Find the share of Shyam.
1. 2088
2. 2000
3. 3087
4. None of these
Ans : C
Geometry
1. Find the coordinates of the point which divides the line
joining (5, -2) and (9, 6) internally in the ratio 1 : 3.
1. (6, 0)
2. (6, 3)
3. (0, 6)
4. (3, 6)
Ans : A
2. Find the number of triangles in an octagon.
1. 326
2. 120
3. 56
4. Cannot be determined
Ans : C
3. Find the equation of a line whose intercepts are twice
of the line 3x – 2y – 12 = 0
1. 3x – 2y = 24
2. 2x – 3y = 12
3. 2x – 3y = 24
4. None of these
Ans : A
4. Find the area of the sector covered by the hour hand
after it has moved through 3 hours and the length of the
hour hand is 7cm.
1. 77 sq.cm
2. 38.5 sq.cm
3. 35 sq.cm
4. 70 sq.cm
Ans : B
5. Find the area of the triangle whose vertices are (-6, -2),
(-4, -6), (-2, 5).
1. 36
2. 18
3. 15
4. 30
Ans : C
6. A stairway 10ft high is such that each step accounts for
half a foot upward and one-foot forward. What distance
will an ant travel if it starts from ground level to reach the
top of the stairway?
1. 30 ft
2. 33 ft
3. 10 ft
4. 29 ft
Ans : D
7. Each interior angle of a regular polygon is 120 degrees
greater than each exterior angle. How many sides are
there in the polygon?
1. 6
2. 8
3. 12
4. 3
Ans : C
8. What is the area of the largest triangle that can be
fitted into a rectangle of length â €˜l’ units and width â
€˜w’ units?
1. lw/3
2. (2lw)/3
3. (3lw)/4
4. (lw)/2
Ans : D
9. Which of the following is inCorrect?
1. An incentre is a point where the angle bisectors meet.
2. The median of any side of a triangle bisects the side at right
angle.
3. The point at which the three altitudes of a triangle meet is the
orthocentre
4. The point at which the three perpendicular bisectors meet is the
centre of the circumcircle.
Ans : B
10. A and B are two points with the co-ordinates (-2, 0)
and (0, 5). What is the length of the diagonal AC if AB form
one of the sides of the square ABCD?
1. units
2. units
3. units
4. units
Ans : B
Second Paper:
1. How long will Lucy have to wait before for her $2,500
invested at 6% earns $600 in simple interest?
A. 2 years
B. 3 years
C. 4 years
D. 5 years
E. 6 years
2. Grace has 16 jellybeans in her pocket. She has 8 red
ones, 4 green ones, and 4 blue ones. What is the
minimum number of jellybeans she must take out of her
pocket to ensure that she has one of each color?
A. 4
B. 8
C. 12
D. 13
E. 16
3. If r = 5 z then 15 z = 3 y, then r =
A. y
B. 2 y
C. 5 y
D. 10 y
E. 15 y
4. What is 35% of a number if 12 is 15% of a number?
A. 5
B. 12
C. 28
D. 33
E. 62
5. A computer is on sale for $1600, which is a 20%
discount off the regular price. What is the regular price?
A. $1800
B. $1900
C. $2000
D. $2100
E. $2200
6. A car dealer sells a SUV for $39,000, which represents
a 25% profit over the cost. What was the cost of the SUV
to the dealer?
A. $29,250
B. $31,200
C. $32,500
D. $33,800
E. $33,999
7. After having to pay increased income taxes this year,
Edmond has to sell his BMW. Edmond bought the car for
$49,000, but he sold it for a 20% loss. What did Edmond
sell the car for?
A. $24,200
B. $28,900
C. $35,600
D. $37,300
E. $39,200
8. If Sam can do a job in 4 days that Lisa can do in 6 days
and Tom can do in 2 days, how long would the job take if
Sam, Lisa, and Tom worked together to complete it?
A. 0.8 days
B. 1.09 days
C. 1.23 days
D. 1.65 days
E. 1.97 days
9. Find 0.12 ÷12
A. 100
B. 10
C. 1
D. 0.01
E. 0.001
10. Divide x5 by x2
A. x25
B. x10
C. x7
D. x3
E. x2.5
11. Which of the following numbers could be described in
the following way: an integer that is a natural, rational and
whole number?
A. 0
B. 1
C. 2.33
D. -3
E. none of the above
12. Find the mode of the following list of numbers: 2, 4, 6,
4, 8, 2, 9, 4, 3, 8
A. 2
B. 3
C. 4
D. 5
E. 6
13. In the fraction 3/x, x may not be substituted by which
of the following sets?
A. {1, 2, 4}
B. {-2,-3,-4}
C. {1, 3, 7}
D. {0, 10, 20}
E. {1.8, 4.3}
14. Sarah needs to make a cake and some cookies. The
cake requires 3/8 cup of sugar and the cookies require 3/5
cup of sugar. Sarah has 15/16 cups of sugar. Does she
have enough sugar, or how much more does she need?
A. She has enough sugar.
B. She needs 1/8 of a cup of sugar.
C. She needs 3/80 of a cup of sugar.
D. She needs 4/19 of a cup of sugar.
E. She needs 1/9 of a cup of sugar.
15. At a company fish fry, 1/2 in attendance are
employees. Employees ’ spouses are 1/3 of the
attendance. What is the percentage of the people in
attendance who are not employees or employee
spouses?
A. 10.5%
B. 16.7%
C. 25%
D. 32.3%
E. 38%
16. In a college, some courses contribute more towards
an overall GPA than other courses. For example, a
science class is worth 4 points; mathematics is worth 3
points; History is worth 2 points; and English is worth 3
points. The values of the grade letters are as follows, A=
4, B=3, C=2, D=1, F=0. What is the GPA of a student who
made a “C” in Trigonometry, a “B” in American
History, an “A” in Botany, and a “B” in
Microbiology?
A. 2.59
B. 2.86
C. 3.08
D. 3.33
E. 3.67
17. There are 8 ounces in a ½ pound. How many ounces
are in 7 3/4 lbs?
A. 12 ounces
B. 86 ounces
C. 119 ounces
D. 124 ounces
E. 138 ounces
18. If the value of x and y in the fraction XZ/Y are both
tripled, how does the value of the fraction change?
A. increases by half
B. decreases by half
C. triples
D. doubles
E. remains the same
19. What is the next number in the following pattern? 1,
1/2, 1/4, 1/8, ___
A. 1/10
B. 1/12
C. 1/14
D. 1/15
E. 1/16
20. Of the following units which would be more likely
used to measure the amount of water in a bathtub?
A. kilograms
B. liters
C. milliliters
D. centigrams
E. volts
21. If a match box is 0.17 feet long, what is its length in
inches the most closely comparable to the following?
A. 5 1/16 inch highlighter
B. 3 1/8 inch jewelry box
C. 2 3/4 inch lipstick
D. 2 3/16 inch staple remover
E. 4 1/2 inch calculator
22. Which of the following fractions is the equivalent of
0.5%?
A. 1/20
B. 1/200
C. 1/2000
D. 1/5
E. 1/500
23. In the graph below, no axes or origin is shown. If
point B ’s coordinates are (10,3), which of the following
coordinates would most likely be A’s?
A. (17, -2)
B. (10, 6)
C. (6,
D. (-10, 3)
E. (-2, -17)
24. Over the course of a week, Fred spent $28.49 on
lunch. What was the average cost per day?
A. $4.07
B. $3.57
C. $6.51
D. $2.93
E. $5.41
25. Of the following units, which would be most likely to
measure the amount of sugar needed in a recipe for 2
dozen cookies?
A. degrees Celsius
B. milliliters
C. quarts
D. kilograms
E. cups
26. Jim has 5 pieces of string. He needs to choose the
piece that will be able to go around his 36-inch waist. His
belt broke, and his pants are falling down. The piece
needs to be at least 4 inches longer than his waist so he
can tie a knot in it, but it cannot be more that 6 inches
longer so that the ends will not show from under his shirt.
Which of the following pieces of string will work the
best?
A. 3 4/5 feet
B. 3 2/3 feet
C. 3 3/8 feet
D. 3 1/4 feet
E. 2 1/2 feet
27. After purchasing a flat screen television for $750, John
realizes that he got a great deal on it and wishes to sell it
for a 15% profit. What should his asking price be for the
television?
A. $800.30
B. $833.60
C. $842.35
D. $862.50
E. $970.25
28. If 300 jellybeans cost you x dollars. How many
jellybeans can you purchase for 50 cents at the same
rate?
A. 150/x
B. 150x
C. 6x
D. x/6
E. 1500x
29. If 6 is 24% of a number, what is 40% of the same
number?
A. 8
B. 10
C. 15
D. 20
E. 25
30. Lee worked 22 hours this week and made $132. If she
works 15 hours next week at the same pay rate, how
much will she make?
A. $57
B. $90
C. $104
D. $112
E. $122
31. The last week of a month a car dealership sold 12 cars.
A new sales promotion came out the first week of the
next month and the sold 19 cars that week. What was the
percent increase in sales from the last week of the
previous month compared to the first week of the next
month?
A. 58%
B. 119%
C. 158%
D. 175%
E. 200%
32. If 8x + 5x + 2x + 4x = 114, the 5x + 3 =
A. 12
B. 25
C. 33
D. 47
E. 86
33. If two planes leave the same airport at 1:00 PM, how
many miles apart will they be at 3:00 PM if one travels
directly north at 150 mph and the other travels directly
west at 200 mph?
A. 50 miles
B. 100 miles
C. 500 miles
D. 700 miles
E. 1,000 miles
34. What is the cost in dollars to steam clean a room W
yards wide and L yards long it the steam cleaners charge
10 cents per square foot?
A. 0.9WL
B. 0.3WL
C. 0.1WL
D. 9WL
E. 3WL
35. Find 8.23 x 109
A. 0.00000000823
B. 0.000000823
C. 8.23
D. 8230000000
E. 823000000000
36. During a 5-day festival, the number of visitors tripled
each day. If the festival opened on a Thursday with 345
visitors, what was the attendance on that Sunday?
A. 345
B. 1,035
C. 1,725
D. 3,105
E. 9,315
37. Which of the following has the least value?
A. 0.27
B. 1/4
C. 3/8
D. 2/11
E. 11%
39. Which year did the same number of boys and girls
attend the conference?
A. 1995
B. 1996
C. 1997
D. 1998
E. None
40. Which two years did the least number of boys attend
the convention?
A. 1995 and 1996
B. 1995 and 1998
C. 1996 and 1997
D. 1997 and 1994
E. 1997 and 1998
Answer Key
1. C 2. D 3. A 4. C 5. C 6. B 7. E 8. B 9. D 10. D 11. B 12. C 13. D
14. C 15. B 16. C 17. D 18. E 19. E 20. B 21. D 22. B 23. C 24. A
25. E 26. C 27. D 28. A 29. B 30. B 31. A 32. C 33. C 34. A 35.
D 36. E 37. E 38. A 39. A 40. A