SA MAH TEST

1. WORD
PROBLEMS
RATES – WORK
Q U A N T I T A T I V E R E A S O N I N G

2. Questio
nP is the set of positive integer factors of 20, and Q is the set
of positive integer factors of 12. If x is a member of set P and
y is a member of set Q what is the greatest possible value of
x-y?
4
8
14
19
20

3. Questio
nOf the students in a certain homeroom, 9 are in the school
play, 12 are in the orchestra, and 15 are in the choral group.
If 5 students participate in exactly 2 of the 3 activities and all
other students participate in only 1 activity, how many
students are in the homeroom?
A. 30
B. 31
C. 26
D. 25
E. 21

4. Step 1
H o w t o a p p r o a c h w o r k
t i m e q u e s t i o n s ?

5. If each student participated in only 1 activity, there would be 9 + 12 + 15 = 36
students in the homeroom.
However, 5 of the students participate in 2 activities.
Therefore, 5 students are counted twice in the sum.
Since these students must be counted only once, the number of students in the
homeroom is
36 - 5 = 31
Choice (B) is correct
How long will A alone take to complete the
task?A and B working together take 12 days. B alone takes 60
days

6. Understanding relation between time taken and rate
· If A takes ‘a’ days to complete a
task
01
How long will A alone take to complete the
task?A and B working together take 12 days. B alone takes 60
days

7. Understanding relation between time taken and rate
· If A takes ‘a’ days to complete a
task
a
A will complete
1
of the task in a
day
01
How long will A alone take to complete the
task?A and B working together take 12 days. B alone takes 60
days

8. Understanding relation between time taken and rate
· If A takes ‘a’ days to complete a
task
a
A will complete
1
of the task in a
day
Therefore, if A takes 20 days and B
takes 30 days to complete a task, it
will be absurd to say that working
together they will take 20 + 30 = 50
days.

01
How long will A alone take to complete the
task?A and B working together take 12 days. B alone takes 60
days

9. Understanding relation between time taken and rate
· If A takes ‘a’ days to complete a
task
a
A will complete
1
of the task in a
day
Therefore, if A takes 20 days and B
takes 30 days to complete a task, it
will be absurd to say that working
together they will take 20 + 30 = 50
days.
  20
In a day A will complete 1 th of the task
and 1
B will complete 30th of the
task.
Together they will complete 1 + 1 = 3+2 = 1
20 30 60 12
Or they will complete the task in 12
days.
01
How long will A alone take to complete the
task?A and B working together take 12 days. B alone takes 60
days

10. Understanding relation between time taken and rate. Continued….01
How long will A alone take to complete the
task?A and B working together take 12 days. B alone takes 60
days

11. Understanding relation between time taken and rate. Continued….
Similarly, if A takes ‘a’ days to
complete a task and B takes ‘b’ days
to complete a task and if working
together they will complete the task in
10 days,
it is INCORRECT to say a + b = 10.

01
How long will A alone take to complete the
task?A and B working together take 12 days. B alone takes 60
days

12. Understanding relation between time taken and rate. Continued….
Similarly, if A takes ‘a’ days to
complete a task and B takes ‘b’ days
to complete a task and if working
together they will complete the task in
10 days,
it is INCORRECT to say a + b = 10.
  The correct expression
is 1
1 1
a+ b = 10
01
How long will A alone take to complete the
task?A and B working together take 12 days. B alone takes 60
days

13. Understanding relation between time taken and rate. Continued….
Only the rate of work done in a day by two people
working together can be added or subtracted. The time
taken individually should not be added or subtracted.
Similarly, if A takes ‘a’ days to
complete a task and B takes ‘b’ days
to complete a task and if working
together they will complete the task in
10 days,
it is INCORRECT to say a + b = 10.
  The correct expression
is 1
1 1
a+ b = 10
01
How long will A alone take to complete the
task?A and B working together take 12 days. B alone takes 60
days

14. Step 2
Frame equation; solveequation

15. How long will A alone take to complete the
task?A and B working together take 12 days. B alone takes 60
days
· Working alone, let A take ‘a’ days to complete
the task.

16. How long will A alone take to complete the
task?A and B working together take 12 days. B alone takes 60
days
· Working alone, let A take ‘a’ days to complete
the task. a
A will complete
1
of the task in a
day.

17. How long will A alone take to complete the
task?A and B working together take 12 days. B alone takes 60
days
Working alone, let A take ‘a’ days to complete
the task.
Working alone, B take 60 days to complete
the task.
a
A will complete
1
of the task in a
day.
·
·

18. How long will A alone take to complete the
task?A and B working together take 12 days. B alone takes 60
days
Working alone, let A take ‘a’ days to complete
the task.
Working alone, B take 60 days to complete
the task.
a
A will complete
1
of the task in a
day.
·
·
60
B will complete
1
of the task in a
day.

19. How long will A alone take to complete the
task?A and B working together take 12 days. B alone takes 60
days
Working alone, let A take ‘a’ days to complete
the task.
Working alone, B take 60 days to complete
the task.
a
A will complete
1
of the task in a
day.
·
·
60
B will complete
1
of the task in a
day.
· a 60
Working together A and B will complete
1
+
1
ofthe task in a
day.

20. How long will A alone take to complete the
task?A and B working together take 12 days. B alone takes 60
days
Working alone, let A take ‘a’ days to complete
the task.
Working alone, B take 60 days to complete
the task.
a
A will complete
1
of the task in a
day.
·
·
60
B will complete
1
of the task in a
day.
· a 60
Working together A and B will complete
1
+
1
ofthe task in a
day.
Working together A and B take 12
days.

21. How long will A alone take to complete the
task?A and B working together take 12 days. B alone takes 60
days
Working alone, let A take ‘a’ days to complete
the task.
Working alone, B take 60 days to complete
the task.
a
A will complete
1
of the task in a
day.
·
·
60
B will complete
1
of the task in a
day.
· a 60
Working together A and B will complete
1
+
1
ofthe task in a
day.
Working together A and B take 12
days.
12
 they complete
1
of the task in a day
.

22. How long will A alone take to complete the
task?A and B working together take 12 days. B alone takes 60
days
Working alone, let A take ‘a’ days to complete
the task.
Working alone, B take 60 days to complete
the task.
a
A will complete
1
of the task in a
day.
·
·
60
B will complete
1
of the task in a
day.
· a 60
Working together A and B will complete
1
+
1
ofthe task in a
day.
Working together A and B take 12
days.
·
12
 they complete
1
of the task in a day
.
Equating the two,
1
+
1
=
1
a 60 12

23. How long will A alone take to complete the
task?A and B working together take 12 days. B alone takes 60
days
Working alone, let A take ‘a’ days to complete
the task.
Working alone, B take 60 days to complete
the task.
a
A will complete
1
of the task in a
day.
·
·
60
B will complete
1
of the task in a
day.
· a 60
Working together A and B will complete
1
+
1
ofthe task in a
day.
Working together A and B take 12
days.
·
12
 they complete
1
of the task in a day
.
Equating the two,
1
+
1
=
1
a 60 12 Or
1
=
1
-
1
a 12 60

24. How long will A alone take to complete the
task?A and B working together take 12 days. B alone takes 60
days
Working alone, let A take ‘a’ days to complete
the task.
Working alone, B take 60 days to complete
the task.
a
A will complete
1
of the task in a
day.
·
·
60
B will complete
1
of the task in a
day.
· a 60
Working together A and B will complete
1
+
1
ofthe task in a
day.
Working together A and B take 12
days.
·
12
 they complete
1
of the task in a day
.
Equating the two,
1
+
1
=
1
a 60 12 Or
1
=
1
-
1
a 12 60
1 = 5 - 1 = 4 = 1
a 60 60 15

25. A takes 15 days
How long will A alone take to complete the
task?A and B working together take 12 days. B alone takes 60
days
Working alone, let A take ‘a’ days to complete
the task.
Working alone, B take 60 days to complete
the task.
a
A will complete
1
of the task in a
day.
·
·
60
B will complete
1
of the task in a
day.
· a 60
Working together A and B will complete
1
+
1
ofthe task in a
day.
Working together A and B take 12
days.
·
12
 they complete
1
of the task in a day
.
Equating the two,
1
+
1
=
1
a 60 12 Or
1
=
1
-
1
a 12 60
1 = 5 - 1 = 4 = 1
a 60 60 15

26. A takes 15 days
Correct Answer : Choice E
How long will A alone take to complete the
task?A and B working together take 12 days. B alone takes 60
days
Working alone, let A take ‘a’ days to complete
the task.
Working alone, B take 60 days to complete
the task.
a
A will complete
1
of the task in a
day.
·
·
60
B will complete
1
of the task in a
day.
· a 60
Working together A and B will complete
1
+
1
ofthe task in a
day.
Working together A and B take 12
days.
·
12
 they complete
1
of the task in a day
.
Equating the two,
1
+
1
=
1
a 60 12 Or
1
=
1
-
1
a 12 60
1 = 5 - 1 = 4 = 1
a 60 60 15

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28. ACT/SAT
W e o f f e r O N L I N E C L A S S E S
C a l l u s : + 9 2 3 3 3 9 3 0 2 2 5 6
S k y h a w k s 2 f l y
S k y H a w k s A c a d e m y