Numbers(Study by Topics Senior Class) : GATE Academy

Welcome to your Numbers(Senior Class Math Study by Topics)

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1. In a class of 58 students, 35 offer Biology, 28 offer Economics and 15 offer Physics.
Each student offers at least one of the three subjects.
If 12 students offer both Biology and Economics, 7 students offer both Biology and Physics and 5 students offer both Economics and Physics,
how many students offer all three subjects?

2. A grocer sells an article for £54 at a profit of 8%.
What is her percentage profit or loss if she sells the same article for £44?

12% profit

18.5% loss

18.5% profit

12% loss

3. The number 101.011₂ converted to base ten is equal to

5.375

2.200

4.250

3.125

4. Given the universal set U = {2, 3, 4, 5, 6, 7, 8, 9} and
subsets P = {2, 4, 6, 8} and
Q {x : x² < 50, x is odd},

find (P∩Q)

{}

{9}

{0}

5. If X= {1, 2, 3, 4} and
Y = {3, 5, 6},
the elements of (X ∩ Y) ∪ X are

{1,2,3,4}

{3}

{1,2,4}

{3,5,6}

6. If I is the set of positive integers and
P = {x : x ∈ I, x² < 10 and x ≠ 0}, then

P = {0, 1, 2, 3}

P = {0, 1}

P = {1, 2, 3}

P is an infinite set

7. The speed of 144 kilometres per hour, expressed in metres per second is

8. A school went into a sports fiesta with a contingent which includes 11 footballers and 8 sprinters.
If 3 of the footballers are also sprinters, how many of the students are either footballers or sprinters

9. The universal set U contains all integers.
Subsets of U are defined as
P = {x : x ≤ 3}
Q = {x : -5 < x < 12}
R = {x : -2 ≤ x < 5}
P ∩ (Q ∪ R)' is

{}

{x< -4}

{-4

{x<0}

10. The subsets X,Y and Z of a universal set are defined as
X = {a, e, m, p} ;
Y = {a, e, i, o, u} and
Z = {l, m, n, o, p, q, r, s, t, u}
The elements of X ∪ (Y ∩ Z) are

{a, e, m, o, p}

{a, e, m, o, p, u}

{m, p, o, u}

{a, e, m, p, u}

11. If P = {3, 1, 0, 5};
Q = {2, 3, 8, 1, 4} and
R = {7, 6, 5},
then P ∩ Q ∩ R is

{ }

{1}

{1,3,5}

{0}

12. A number of chocolates were shared out among three children Kafeel, Tara and Kameel in the ratio 2:3:4 respectively.

If Kameel got 8, how many sweets were shared out?

13. In a Year 12 class of 45 students, every student has to offer either Chemistry or Economics or both.
If 25 students offer Chemistry while 34 offer Economics,
how many students offer both subjects?

14. The ratio of the price of a tin of milk to that of a packet of sugar is m : p.
If the price of milk now goes up by 25% while that of sugar goes up by 15%,
the new ratio of the prices is

5p : 3m

3p : 5m

25m : 23p

23m : 25p

15. A trader bought 132 oranges at C30 each, and sold them at C42 each,
where C is the currency reckoned in base 4,
the profit is

C2310 base 4

C3210 base 4

C231 base 4

C2210 base 4

16. A sum of money invested at a simple interest rate R increases to 5/3 times the original sum after 5 years.
The value of R is

13.3%

10.5%

6.0%

9.0%

17. When the food bill for a family increased by 20% during a pandemic,
the family head reduced the quantity of food bought for the family by 15%.
The fractional increase in the food bill is now

1/50

7/40

1/20

7/20

18.

110111_two – X_ten = 10101_two, find X

19. A bag contains white, blue and red ping pong balls in the ratio 8 : 3: 2.
There are 10 red balls.
If 10 white and 10 blue balls are removed from the bag,
the new ratio is

7 : 2 : 1

7 : 1 : 2

6 : 1 : 2

6 : 1 : 1

20. A rectangle is formed from a square by increasing the latter's length by 50% while reducing its width by 50%.
The ratio of the area of the rectangle to that of the square is

2 : 3

4 : 3

3 : 4

3 : 2

21. The baking recipe for a piece of brownie cake is given as 1.5 cups of sugar and 3.5 cups of flour.
If a cake is baked, based on this recipe with a total of 40 cups of sugar and flour, the number of cups of sugar used is

22. A businessman invested a total of $200,000 in two companies which paid dividends of 5% and 7% respectively.
If he received a total of $11,600,
how much did he invest at 7%?

$160,000

$80,000

$140,000

$100,000

23. In a Yr 8 class of 60 students in a Nigerian school, 40 speak Hausa while 19 speak Igbo and 7 students speak both languages.
How many students speak neither of the languages?

24. If U = {integers ≤ 20},
X = {multiples of 4},
Y = {multiples of 3}.
The elements of X' ∩ Y are

{12}

{3, 6, 9, 15, 18}

{}

{3, 5, 7}

25. A plumber's daily wage is £80 for the first 10 days and £100 for the next 9 days. Find the daily wage for the remaining 6 working days of the month, if his average daily wage for the month is £90.80

£95

£110

£105

£92.50

26 out of 25

Numbers(Study by Topics Senior Class)

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