Q&A - P5 Math

[MathIzzzFun]

doraemo:

MathIzzzFun:

[quote=\"doraemo\"]Help Needed..


120 boys are standing in front of their lockers, numbered from 1 to 120. At the start, all lockers are opened. A teacher calls out ‘1’, and since 1 is a divisor of all the numbers, all the boys close their lockers. The teacher then calls out ‘2’ , and only those boys whose locker numbers are divisible by 2 will open their lockers. The teacher then calls out ‘3’ . Those boys whose locker numbers are divisible by 3 will open their lockers if they are closed, or close their lockers if they are opened. This process is continued until ‘120’ is called out. How many lockers will be closed at the end of the entire process?

may I know the source of the question - school practice question or MO question ?

10 lockers will be closed.

cheers.

Hi MathIzzzFun
Thank you for your help. MO question.
10 lockers will be closed?[/quote]Yes, 10 lockers (with locker numbers that are square numbers) will be closed.

Since every locker is opened at first, it will stay open if it is opened/closed EVEN number of times, and it will be closed if it opened/closed ODD number of times. Every locker will only be opened/closed when the number called is A FACTOR of the locker number.

ONLY square numbers have odd number of factors (as one of the factor has a twin), all others have even number of factors. So, only locker number which is a square will be closed odd number of times --> closed in the end.

cheers.

[panic_mum]

Hi I need help on these questions …i have been cracking my brains …Thank q…

1) There are a total of 1430 red, blue, green and yellow marbles in a box. John discovers that if he does all of the following :-
.doubles the number of red marbles;
.adds 40 blue marbles;
.removes 30 green marbles and
.removers half the yellow marble
he would get the same number of marbles for each colour.
How many green marbles are there in the box?

[Jamesbond]

Using 3/5 of her money, Chloe could buy 11 notebooks. If she was given an extra $2, she could use it together with the remaining amount of money to buy another 8 such notebooks. How much money did Chloe have?

[tianzhu]

Jamesbond:

Using 3/5 of her money, Chloe could buy 11 notebooks. If she was given an extra $2, she could use it together with the remaining amount of money to buy another 8 such notebooks. How much money did Chloe have?

Hi

3 units ------ 11NB

2 units + 2 ------ 8NB

Make the number of NB equal

24 units ------- 88NB

22 units + 22 ------- 88NB

24 units ------- 22 units + 22

1 unit ------- 11

Chloe --------- 5*11 ------ 55

Best wishes

[tianzhu]

panic_mum:

Hi I need help on these questions ...i have been cracking my brains ...Thank q...

1) There are a total of 1430 red, blue, green and yellow marbles in a box. John discovers that if he does all of the following :-
.doubles the number of red marbles;
.adds 40 blue marbles;
.removes 30 green marbles and
.removers half the yellow marble
he would get the same number of marbles for each colour.
How many green marbles are there in the box?

Hi

It helps to draw MD or you may work using units.

After

Red ----- 2 units (doubles the number of red marbles)
Blue ------ 2 units (adds 40 blue marbles)
Green ------- 2 units (removes 30 green marbles)
Yellow ------- 2 units (removes half the yellow marbles)

Before

Red ----- 1 unit
Blue ------ 2 units – 40
Green ------- 2 units + 30
Yellow ------- 4 units

9 units ------- 1440
1 unit ------- 160

Number of green marbles -------320 + 30 ------- 350

Best wishes

[Trevortan]

1. A survey shows that the students of Chesvoire School come to school either by bus, MRT or by private transport. 2/5 of the students come to school by bus. The remaining students travel to school by MRT and private transport in the ratio 3:4. Given that 180 more students take the school bus than private transport, how many students are there in Chesvoire School?

2. A figure is made up of a rectangle and a square. The ratio of the area of the square to that of the rectangle is 2:5. If 1/4 of the square is shaded, what fraction of the figure is unshaded?
3. Jacintha and Isabel shared a number of cookies in the ratio 2:1. The number of cookies that Jacintha had was 1/4 of the number of cookies Evelyn had. If Evelyn had 63 more cookies than Isabel, how many cookies did the three of them have altogether?
4. In a basket, the ratio of the number of pears to the number of apples is 3:4. If I add another 12 apples, there would be 1/2 as many pears as apples. How many pears and apples are there in the basket at first?
5. Alex, Terence, Cherry and Daniel bought a present for their friend. Alex paid 1/4 of the amount paid by Terence, Cherry and Daniel. The ratio of the amount paid by Terence to the amount paid by Cherry and Daniel was 3:5. The ratio of the amount paid by Cherry to the amount paid by Daniel was 3:7. Given that Alex paid $12 less than Daniel, find the cost of the present.
Thanks a lot.

[Trevortan]

1. A survey shows that the students of Chesvoire School come to school either by bus, MRT or by private transport. 2/5 of the students come to school by bus. The remaining students travel to school by MRT and private transport in the ratio 3:4. Given that 180 more students take the school bus than private transport, how many students are there in Chesvoire School?

2. A figure is made up of a rectangle and a square. The ratio of the area of the square to that of the rectangle is 2:5. If 1/4 of the square is shaded, what fraction of the figure is unshaded?
3. Jacintha and Isabel shared a number of cookies in the ratio 2:1. The number of cookies that Jacintha had was 1/4 of the number of cookies Evelyn had. If Evelyn had 63 more cookies than Isabel, how many cookies did the three of them have altogether?
4. In a basket, the ratio of the number of pears to the number of apples is 3:4. If I add another 12 apples, there would be 1/2 as many pears as apples. How many pears and apples are there in the basket at first?
5. Alex, Terence, Cherry and Daniel bought a present for their friend. Alex paid 1/4 of the amount paid by Terence, Cherry and Daniel. The ratio of the amount paid by Terence to the amount paid by Cherry and Daniel was 3:5. The ratio of the amount paid by Cherry to the amount paid by Daniel was 3:7. Given that Alex paid $12 less than Daniel, find the cost of the present.
:thankyou:

[panic_mum]

Hi how do you get 1440?

[tianzhu]

panic_mum:

Hi how do you get 1440?

Hi

There are a total of 1430 red, blue, green and yellow marbles in a box.

9 units – 40 + 30 ------ 1430

9 units ------ 1440

Best wishes

[tianzhu]

Trevortan:

4. In a basket, the ratio of the number of pears to the number of apples is 3:4. If I add another 12 apples, there would be 1/2 as many pears as apples. How many pears and apples are there in the basket at first?

Hi

Before
Pears:Apples ------ 3:4

After
Pears:Apples ------ 1:2 ------ 3:6

The number of pears stays the same; make its units the same before and after.

2 units ------ 12

1 unit ------ 6

Pears@first -------- 3*6 ------- 18

Appless@first -------- 3*6 ------- 24

Total ------- 42

Best wishes