Numbers(Study by Topics Senior Class) : GATE Academy

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1. If 101010₂= x₁₀+ 1111_2,
the value of x is

2. A sum of N420 is shared among three children in the ratio 6 : 7 : 8.
The largest share is

N160

N140

N180

N120

3. 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 : 1 : 2

7 : 2 : 1

6 : 1 : 1

6 : 1 : 2

4. If U = {5, 6, 7, 8},
P ={6, 7} and
Q = {6, 8},
then, (P∩Q)' is

{6, 7}

{5, 8}

{5, 6, 7}

{5, 7, 8}

5. In a test taken by 40 boys and x girls, the mean scores were 5.5 and 6 respectively for the boys and girls.
If the total score was 412, the value of x is

6. After getting a pay rise of 20%, a man's new annual salary is N21,600.
His salary before the pay rise was

N17,280

N18,000

N17,700

N16,680

7. The ratio of the age of a father to that of his son is 9 : 2.
If the son is now 8 years old,
the ratio of their ages in 4 years time will be

10 : 3

3 : 1

9 : 4

5 : 1

8. 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

£92.50

£105

9. Given that P = {1, 2, 3, 4};
Q ={5, 6, 7, 8} and
R = {1, 2, 3, 2, 4, 2},
it follows that
I. P = R
II. n(R) = 6
III. n(P ∪R) = 4
Which of the statements above is (are) true?

II only

I only

I and III only

III only

10. A worker is allowed 10% of her income tax free and pays 15% on the remainder.
If her tax amounts to $2,970, her income is

$28,000

$20,000

$22,000

$25,000

11. If R = {x : x² = 16, x > 5},
then R is equal to

{0}

{5}

{}

12. A housewife bought five tubers yam at W34 per tuber and three oranges at W5 each where W is the currency reckoned in base six.
The total amount spent by the housewife is

W315 base 6

W225 base 6

W252 base 6

W352 base 6

13. If 45% of the Nigerian naira (N) is equal to 35% of a foreign currency $,
the conversion rate of $ to N is $1 =

N 20/7

N 9/7

N 7/9

N 20/9

14. 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

1/20

7/20

1/50

7/40

15. 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

12% loss

18.5% loss

18.5% profit

16. In a certain class, 37 students take at least one of Chemistry, Economics and History.
8 students take Chemistry, 19 take Economics and 25 take History.
12 students take Economics and History but nobody takes Chemistry and Economics .
How many students take both Chemistry and History?

17. A sum of £50,000 was invested by two partners in a project which yielded £90,000. If the profit was shared in the ratio 3 : 5, the difference between the amounts received by the partners is

£25,000

£15,000

£10,000

£40,000

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

{1}

{ }

{0}

{1,3,5}

19. If 32_x = 20_ten,
the value of x is

20. Two friends Tyson and Kourtney went out to lunch at a restaurant.
If Tyson contributed 40% of the cost and Kourtney contributed the balance,
which is $150, the cost of the lunch was

$260

$375

$250

$300

21. A man bought a wrist watch for $750.00 and re-sold it for $600.00.
His percentage loss was?

25%

15%

20%

22.5%

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

4.250

2.200

5.375

3.125

23. 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?

24. If A : B = 3 : 4 and M : N = 2 : 5,

find A/M : B/N

3:10

15:8

8:15

10:3

25. Convert 69₁₀to a number in base two

100101

1000101

1001101

1010001

26 out of 25

Numbers(Study by Topics Senior Class)

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