Get the Knowledge that sets you free...
Science & Math for K6 - K12 Students
| Exercise-IV |
| 1. |
If 2x + 4y = 28 and  find x |
| Sol: |
8y |
= |
24x |
| |
y |
= |
3x |
| |
2x + 4y |
= |
28 |
| |
2x + 4(3x) |
= |
28 |
| |
14x |
= |
28 |
| |
x |
= |
2 |
| |
Grid form is |
| |
 |
|
|
| |
| 2. |
If  find x |
| Sol: |
 |
= |
 |
| |
10(x – 2) |
= |
6(x + 2) |
| |
10x – 20 |
= |
6x + 12 |
| |
4x |
= |
32 |
| |
x |
= |
8 |
| |
Grid form is |
| |
 |
|
|
| |
| 3. |
42 drums contain a total of 17640 litres of water. If each bottle contains the same amount of water, how many litres of water are in each drum |
| Sol: |
42 drums contains 17640 litres of water |
| |
1 drum contains ? litres of water |
| |
 |
= |
420 litres of water |
| |
1 drum contains 420 litres |
| |
Grid form is |
| |
 |
|
|
| |
| 4. |
A Philharmonic orchestra will choose 5 wow singers from its apprentice program. The apprentice program is made of 8 women and 4 men. If 4 women and 1 man are to be chosen from the singer, how many different groupings are possible? |
| Sol: |
There are 8 women total to choose from and the company needs 4, so you would do 8 × 7 × 6 × 5 = 1180 |
| |
However because order doesn't matter to get rid of duplicates. Mathematically this is done by dividing your answer by the factorial of spaces you need to fill |
| |
Because we need 4, we divide by 4! or 24 which leaves us with 70 (1680  24 = 70). |
| |
Now on, to the men. There are 4 men to choose and we need only 1. so there are 4 ways to choose that. |
| |
Now that we have to count (70) women and our men are 4 |
| |
Remember in probability that and means multiply 70 × 4 = 280, which is the answer |
| |
Grid form is |
| |
 |
|
|
| |
| 5. |
The estimated population of snow leapords in a certain region is given by the function p(t) = xt + 200 where t is an integer which represents the number of years after the snow leapord population was counted 0 ≤ t ≤ 20, and 'x' is a constant. If there were 600 snow leapords after 4 yrs the population was first counted, how many snow leapords will there be 12 years after the population was first counted? |
| Sol: |
p(t) |
= |
xt + 200 (put t = 4 , p(t) = 600) |
| |
600 |
= |
x × 4 + 200 |
| |
600 – 200 |
= |
4x |
| |
4x |
= |
400 |
| |
x |
= |
100 leapords |
| |
p(t) |
= |
xt + 200 (put t = 12 , x = 100) |
| |
p(12) |
= |
12(100) + 200 |
| |
|
= |
1400 |
|
|
| |
| 6. |
x , y , z are the radius of circles where x = 2y = 6y. If perimeter of the shaded region is 70 πcm. Find the length of AF |
| Sol: |
πr1 + πr2 + πr3 |
= |
70π |
| |
Where r1 = x = 42cm , r2 = 2y = 42cm → y = 21cm , r3 = 6z = 42cm → z = 7cm |
| |
AF |
= |
2z + 2y + 2x + 2y + 2z |
| |
|
= |
4y + 4z + 2x |
| |
|
= |
4 × 21 + 4 × 7 + 2 × 42 |
| |
|
= |
84 + 28 + 84 |
| |
|
= |
196cm |
| |
Grid form is |
| |
 |
|
|
| |
| 7. |
There are some birds in a bird sanctuary.  of the birds are flight less.  of the flight less birds have white wings. What % is the percentage of birds which do not have white wings.(The birds which can fly have no white wings) |
| Sol: |
Let the number of birds be 500 |
| |
Number of flight less birds |
= |
 |
| |
|
= |
300 |
| |
Number of flight less birds which have white wings |
= |
 |
| |
|
= |
75 |
| |
Number of birds which do not have white wings |
= |
300 – 75 |
| |
|
= |
225 |
| |
% of birds which do not have white wings |
= |
 |
| |
|
= |
45% |
| |
Grid form is |
| |
 |
|
|
| |
| 8. |
139 persons have for an elimination tournament. All players are to be paired up for the first round, but because 139 is an odd number one player gets a bye, which promotes him to the second round without actually playing in the first round. The pairing continues on the next round, with a bye to any player left over. If the schedule is planned so that a minimum number of matches is required to determine the champion, the number of matches which must be played is |
| Sol: |
Required number of matches will be |
= |
139 – 1 |
| |
|
= |
138 |
| |
Grid form is |
| |
 |
|
|
SAT Math