SAT -MATHS QUESTIONS EASY WAY TO MASTER MATHS FOR ADMISSION EXAMS

1. G M A T Q U A N T I T A T I V E
R E A S O N I N G
NUMBER PROPERTIES
REMAINDERS
DATA SUFFICIENCY
SAT/ACT
Series

2. Questio
n
What is the remainder when the positive integer x is
divided by 6?
1. When x is divided by 7, the remainder is 5.
2. When x is divided by 9, the remainder is 3.
AnswCombinStatementStatementApproacQuestionQuestio

3. ◴Answer these questions before evaluating the statements.
Determine approach to solve the question
Step 1

4. Before going to the
statements
Spend a few seconds answering the following questions
When is the data
sufficient?
Questio Question Approac Statement Statement Combin Answ

5. Before going to the
statements
Spend a few seconds answering the following questions
When is the data
sufficient?
The data is sufficient
when we are able to
find a unique
remainder.
Questio Question Approac Statement Statement Combin Answ

6. Before going to the
statements
Spend a few seconds answering the following questions
When is the data
sufficient?
When is it not sufficient?
The data is sufficient
when we are able to
find a unique
remainder.
Questio Question Approac Statement Statement Combin Answ

7. Before going to the
statements
Spend a few seconds answering the following questions
When is the data
sufficient?
When is it not sufficient?
The data is sufficient
when we are able to
find a unique
remainder.
The data is NOT sufficient
when we get more than
one remainder using the
information in the
statements
Questio Question Approac Statement Statement Combin Answ

8. Before going to the
statements
Spend a few seconds answering the following questions
When is the data
sufficient?
When is it not sufficient? What do we know about x?
The data is sufficient
when we are able to
find a unique
remainder.
The data is NOT sufficient
when we get more than
one remainder using the
information in the
statements
Questio Question Approac Statement Statement Combin Answ

9. Before going to the
statements
Spend a few seconds answering the following questions
When is the data
sufficient?
When is it not sufficient? What do we know about x?
The data is sufficient
when we are able to
find a unique
remainder.
The data is NOT sufficient
when we get more than
one remainder using the
information in the
statements
x is a positive integer
Questio Question Approac Statement Statement Combin Answ

10. Approach to solve the
question
Look for a counter example
Look for a
counter
example
Questio Question Approac Statement Statement Combin Answ

11. Approach to solve the
question
Look for a counter example
Look for a counter
example
If a counter
example exists
data NOTsufficient
Questio Question Approac Statement Statement Combin Answ

12. Approach to solve the
question
Look for a counter example
Look for a counter
example
If a counter
example exists
data NOTsufficient
If a counter
example does not
exist data sufficient
Questio Question Approac Statement Statement Combin Answ

13. Approach to solve the
question
Look for a counter example
Look for a counter
example
If a counter
example exists
data NOTsufficient
If a counter
example does not
exist data sufficient
What is a counter
example?
Questio Question Approac Statement Statement Combin Answ

14. Approach to solve the
question
Look for a counter example
Look for a counter
example
If a counter
example exists
data NOTsufficient
If a counter
example does not
exist data sufficient
What is a counter example?
Find two values for x satisfying information
in the statement, each one resulting in a
different remainder when divided by 6.
Questio Question Approac Statement Statement Combin Answ

15. Approach to solve the
question
Look for a counter example
Look for a counter
example
If a counter
example exists
data NOTsufficient
If a counter
example does not
exist data sufficient
What is a counter example?
Find two values for x satisfying information
in the statement, each one resulting in a
different remainder when divided by 6.
If two such values exist then a counter
example exists
Questio Question Approac Statement Statement Combin Answ

16. Approach to solve the
question
Look for a counter example
Look for a counter
example
If a counter
example exists
data NOTsufficient
If a counter
example does not
exist data sufficient
What is a counter example?
Find two values for x satisfying information
in the statement, each one resulting in a
different remainder when divided by 6.
If two such values exist then a counter
example exists
If for all x satisfying information in the
statement, the remainder is unique – a
counter example does not exist.
Questio Question Approac Statement Statement Combin Answ

17. ◴Evaluate Statement 1 alone
Step 2

18. What is the remainder when the positive integer x is divided
by 6?Lets evaluate statement 1 : When x is divided by 7, the
remainder is 5.
Look fora
counter
example
Questio Question Approac Statement Statement Combin Answ

19. What is the remainder when the positive integer x is divided
by 6?Lets evaluate statement 1 : When x is divided by 7, the
remainder is 5.
Look fora
counter
example
1
 x = 5
Leaves a
remainder of 5
when divided by
7.
Questio Question Approac Statement Statement Combin Answ

20. What is the remainder when the positive integer x is divided
by 6?Lets evaluate statement 1 : When x is divided by 7, the
remainder is 5.
Look fora
counter
example
1
 x = 5
Leaves a
remainder of 5
when divided by
7.
Leaves a
remainder of 5
when divided by
6.
Questio Question Approac Statement Statement Combin Answ

21. What is the remainder when the positive integer x is divided
by 6?Lets evaluate statement 1 : When x is divided by 7, the
remainder is 5.
Look fora
counter
example
1
 x = 5
Leaves a
remainder of 5
when divided by
7.
Leaves a
remainder of 5
when divided by
6.
How do we find the next number
that satisfies statement 1?
Values satisfying first statement will be
in an Arithmetic progression. First term
is 5 and common difference is 7. The
sequence is 5, 12, 19, 26 …..
Questio Question Approac Statement Statement Combin Answ

22. What is the remainder when the positive integer x is divided
by 6?Lets evaluate statement 1 : When x is divided by 7, the
remainder is 5.
Look fora
counter
example
1
 x = 5
Leaves a
remainder of 5
when divided by
7.
Leaves a
remainder of 5
when divided by
6.
How do we find the next number
that satisfies statement 1?
Values satisfying first statement will be
in an Arithmetic progression. First term
is 5 and common difference is 7. The
sequence is 5, 12, 19, 26 …..
Lets find out the remainder when x =
12
Questio Question Approac Statement Statement Combin Answ

23. What is the remainder when the positive integer x is divided
by 6?Lets evaluate statement 1 : When x is divided by 7, the
remainder is 5.
Look fora
counter
example
1 2
 x = 5
Leaves a
remainder of 5
when divided by
7.
Leaves a
remainder of 5
when divided by
6.
 x = 12
Leaves a
remainder of 5
when divided by
7.
Questio Question Approac Statement Statement Combin Answ

24. What is the remainder when the positive integer x is divided
by 6?Lets evaluate statement 1 : When x is divided by 7, the
remainder is 5.
Look fora
counter
example
1 2
 x = 5
Leaves a
remainder of 5
when divided by
7.
Leaves a
remainder of 5
when divided by
6.
 x = 12
Leaves a
remainder of 5
when divided by
7.
Leaves a
remainder of 0
when divided by
6.
Questio Question Approac Statement Statement Combin Answ

25. What is the remainder when the positive integer x is divided
by 6?Lets evaluate statement 1 : When x is divided by 7, the
remainder is 5.
Look fora
counter
example
1 2
 x = 5
Leaves a
remainder of 5
when divided by
7.
Leaves a
remainder of 5
when divided by
6.
 x = 12
Leaves a
remainder of 5
when divided by
7.
Leaves a
remainder of 0
when divided by
6.
Counter
example exists
Statement 1
alone is NOT
sufficient
Questio Question Approac Statement Statement Combin Answ

26. What is the remainder when the positive integer x is divided
by 6?Lets evaluate statement 1 : When x is divided by 7, the
remainder is 5.
Look fora
counter
example
1 2
 x = 5
Leaves a
remainder of 5
when divided by
7.
Leaves a
remainder of 5
when divided by
6.
 x = 12
Leaves a
remainder of 5
when divided by
7.
Leaves a
remainder of 0
when divided by
6. Eliminate
choices A and D
Counter
example exists
Statement 1
alone is NOT
sufficient
Questio Question Approac Statement Statement Combin Answ

27. What is the remainder when the positive integer x is divided
by 6?Lets evaluate statement 1 : When x is divided by 7, the
remainder is 5.
Look fora
counter
example
1 2
 x = 5
Leaves a
remainder of 5
when divided by
7.
Leaves a
remainder of 5
when divided by
6.
 x = 12
Leaves a
remainder of 5
when divided by
7.
Leaves a
remainder of 0
when divided by
6. Eliminate
choices A and D
Choices narrow
down to B, C or E.
Counter
example exists
Statement 1
alone is NOT
sufficient
Questio Question Approac Statement Statement Combin Answ

28. ◴Evaluate Statement 2 alone
Step 3

29. What is the remainder when the positive integer x is divided
by 6?Lets evaluate statement 2 : When x is divided by 9, the
remainder is 3.
Look fora
counter
example
1
 x = 3
Leaves a
remainder of 3
when divided by
9.
Questio Question Approac Statement Statement Combin Answ

30. What is the remainder when the positive integer x is divided
by 6?Lets evaluate statement 2 : When x is divided by 9, the
remainder is 3.
Look fora
counter
example
1
 x = 3
Leaves a
remainder of 3
when divided by
9.
Leaves a
remainder of 3
when divided by
6.
Questio Question Approac Statement Statement Combin Answ

31. What is the remainder when the positive integer x is divided
by 6?Lets evaluate statement 2 : When x is divided by 9, the
remainder is 3.
Look fora
counter
example
1
 x = 3
Leaves a
remainder of 3
when divided by
9.
Leaves a
remainder of 3
when divided by
6.
How do we find the next number
that satisfies statement 2?
Values satisfying second statement will
be in an Arithmetic progression. First
term is 3 and common difference is 9.
The sequence is 3, 12, 21, 30 …..
Questio Question Approac Statement Statement Combin Answ

32. What is the remainder when the positive integer x is divided
by 6?Lets evaluate statement 2 : When x is divided by 9, the
remainder is 3.
Look fora
counter
example
1
 x = 3
Leaves a
remainder of 3
when divided by
9.
Leaves a
remainder of 3
when divided by
6.
How do we find the next number
that satisfies statement 2?
Values satisfying second statement will
be in an Arithmetic progression. First
term is 3 and common difference is 9.
The sequence is 3, 12, 21, 30 …..
Questio Question Approac Statement Statement Combin Answ
Lets find out the remainder when x =
12

33. What is the remainder when the positive integer x is divided
by 6?Lets evaluate statement 2 : When x is divided by 9, the
remainder is 3.
Look fora
counter
example
1 2
 x = 3
Leaves a
remainder of 3
when divided by
9.
Leaves a
remainder of 3
when divided by
6.
 x = 12
Leaves a
remainder of 3
when divided by
9.
Questio Question Approac Statement Statement Combin Answ

34. What is the remainder when the positive integer x is divided
by 6?Lets evaluate statement 2 : When x is divided by 9, the
remainder is 3.
Look fora
counter
example
1 2
 x = 3
Leaves a
remainder of 3
when divided by
9.
Leaves a
remainder of 3
when divided by
6.
 x = 12
Leaves a
remainder of 3
when divided by
9.
Leaves a
remainder of 0
when divided by
6.
Questio Question Approac Statement Statement Combin Answ

35. What is the remainder when the positive integer x is divided
by 6?Lets evaluate statement 2 : When x is divided by 9, the
remainder is 3.
Look fora
counter
example
1 2
 x = 3
Leaves a
remainder of 3
when divided by
9.
Leaves a
remainder of 3
when divided by
6.
 x = 12
Leaves a
remainder of 3
when divided by
9.
Leaves a
remainder of 0
when divided by
6.
Counter
example exists
Statement 2
alone is NOT
sufficient
Questio Question Approac Statement Statement Combin Answ

36. What is the remainder when the positive integer x is divided
by 6?Lets evaluate statement 2 : When x is divided by 9, the
remainder is 3.
Look fora
counter
example
1 2
 x = 3
Leaves a
remainder of 3
when divided by
9.
Leaves a
remainder of 3
when divided by
6.
 x = 12
Leaves a
remainder of 3
when divided by
9.
Leaves a
remainder of 0
when divided by
6. Eliminate
choice B as well
Counter
example exists
Statement 2
alone is NOT
sufficient
Questio Question Approac Statement Statement Combin Answ

37. What is the remainder when the positive integer x is divided
by 6?Lets evaluate statement 2 : When x is divided by 9, the
remainder is 3.
Look fora
counter
example
1 2
 x = 3
Leaves a
remainder of 3
when divided by
9.
Leaves a
remainder of 3
when divided by
6.
 x = 12
Leaves a
remainder of 3
when divided by
9.
Leaves a
remainder of 0
when divided by
6. Eliminate
choice B as well
Choices narrow
down to C or E.
Counter
example exists
Statement 2
alone is NOT
sufficient
Questio Question Approac Statement Statement Combin Answ

38. ◴Evaluate the data given in the two statements together
Step 4

39. What is the remainder when the positive integer x is divided
by 6?x is divided by 7, the remainder is 5. x is divided by 9, the
remainder is 3.
Look fora
counter
example
 x = 12
Leaves a
remainder of 5
when divided by
7.
Questio Question Approac Statement Statement Combin Answ

40. What is the remainder when the positive integer x is divided
by 6?x is divided by 7, the remainder is 5. x is divided by 9, the
remainder is 3.
Look fora
counter
example
 x = 12
Leaves a
remainder of 5
when divided by
7.
Leaves a
remainder of 3
when divided by
9.
Questio Question Approac Statement Statement Combin Answ

41. What is the remainder when the positive integer x is divided
by 6?x is divided by 7, the remainder is 5. x is divided by 9, the
remainder is 3.
Look fora
counter
example
Leaves a
remainder of 0
when divided by
6.
Questio Question Approac Statement Statement Combin Answ
 x = 12
Leaves a
remainder of 5
when divided by
7.
Leaves a
remainder of 3
when divided by
9.

42. What is the remainder when the positive integer x is divided
by 6?x is divided by 7, the remainder is 5. x is divided by 9, the
remainder is 3.
Look fora
counter
example
Leaves a
remainder of 0
when divided by
6.
 x = 12
Leaves a
remainder of 5
when divided by
7.
Leaves a
remainder of 3
when divided by
9.
How do we find the next number that satisfies
both the statements?
Questio Question Approac Statement Statement Combin Answ

43. What is the remainder when the positive integer x is divided
by 6?x is divided by 7, the remainder is 5. x is divided by 9, the
remainder is 3.
Look fora
counter
example
Leaves a
remainder of 0
when divided by
6.
 x = 12
Leaves a
remainder of 5
when divided by
7.
Leaves a
remainder of 3
when divided by
9.
How do we find the next number that satisfies
both the statements?
Values satisfying first statement are in an Arithmetic
progression. First term is 5 and common difference is 7.
The sequence is 5, 12, 19, 26 …..
Questio Question Approac Statement Statement Combin Answ

44. What is the remainder when the positive integer x is divided
by 6?x is divided by 7, the remainder is 5. x is divided by 9, the
remainder is 3.
Look fora
counter
example
Leaves a
remainder of 0
when divided by
6.
 x = 12
Leaves a
remainder of 5
when divided by
7.
Leaves a
remainder of 3
when divided by
9.
How do we find the next number that satisfies
both the statements?
Values satisfying first statement are in an Arithmetic
progression. First term is 5 and common difference is 7.
The sequence is 5, 12, 19, 26 …..
Questio Question Approac Statement Statement Combin Answ
Values satisfying second statement are in a second
Arithmetic progression. First term is 3 and common
difference is 9. The sequence is 3, 12, 21, 30 …..

45. What is the remainder when the positive integer x is divided
by 6?x is divided by 7, the remainder is 5. x is divided by 9, the
remainder is 3.
Look fora
counter
example
Leaves a
remainder of 0
when divided by
6.
 x = 12
Leaves a
remainder of 5
when divided by
7.
Leaves a
remainder of 3
when divided by
9.
How do we find the next number that satisfies
both the statements?
Values satisfying first statement are in an Arithmetic
progression. First term is 5 and common difference is 7.
The sequence is 5, 12, 19, 26 …..
Questio Question Approac Statement Statement Combin Answ
Values satisfying second statement are in a second
Arithmetic progression. First term is 3 and common
difference is 9. The sequence is 3, 12, 21, 30 …..
Therefore, values common to both statements will be in
an AP.First term will be 12. Common difference will be
the LCM of the two common differences. i.e., LCM of 7
and 9 = 63. The sequence will be 12, 75, 138 …

46. What is the remainder when the positive integer x is divided
by 6?x is divided by 7, the remainder is 5. x is divided by 9, the
remainder is 3.
Look fora
counter
example
Leaves a
remainder of 3
when divided by
9.
Leaves a
remainder of 0
when divided by
6.
 x = 12
Leaves a
remainder of 5
when divided by
7.
 x = 75
Questio Question Approac Statement Statement Combin Answ

47. What is the remainder when the positive integer x is divided
by 6?x is divided by 7, the remainder is 5. x is divided by 9, the
remainder is 3.
Look fora
counter
example
Leaves a
remainder of 3
when divided by
9.
Leaves a
remainder of 0
when divided by
6.
 x = 12
Leaves a
remainder of 5
when divided by
7.
 x = 75
Leaves a
remainder of 5
when divided by
7.
Questio Question Approac Statement Statement Combin Answ

48. What is the remainder when the positive integer x is divided
by 6?x is divided by 7, the remainder is 5. x is divided by 9, the
remainder is 3.
Look fora
counter
example
Leaves a
remainder of 3
when divided by
9.
Leaves a
remainder of 0
when divided by
6.
 x = 12
Leaves a
remainder of 5
when divided by
7.
Leaves a
remainder of 3
when divided by
9.
 x = 75
Leaves a
remainder of 5
when divided by
7.
Questio Question Approac Statement Statement Combin Answ

49. What is the remainder when the positive integer x is divided
by 6?x is divided by 7, the remainder is 5. x is divided by 9, the
remainder is 3.
Look fora
counter
example
Leaves a
remainder of 3
when divided by
9.
Leaves a
remainder of 0
when divided by
6.
 x = 12
Leaves a
remainder of 5
when divided by
7.
Leaves a
remainder of 3
when divided by
9.
Leaves a
remainder of 3
when divided by
6.
 x = 75
Leaves a
remainder of 5
when divided by
7.
Questio Question Approac Statement Statement Combin Answ

50. What is the remainder when the positive integer x is divided
by 6?x is divided by 7, the remainder is 5. x is divided by 9, the
remainder is 3.
Look fora
counter
example
Leaves a
remainder of 3
when divided by
9.
Leaves a
remainder of 0
when divided by
6.
 x = 12
Leaves a
remainder of 5
when divided by
7.
Leaves a
remainder of 3
when divided by
9.
Leaves a
remainder of 3
when divided by
6.
 x = 75
Leaves a
remainder of 5
when divided by
7.
Counter
example exists
Statements
Together are
NOTsufficient
Questio Question Approac Statement Statement Combin Answ

51. What is the remainder when the positive integer x is divided
by 6?x is divided by 7, the remainder is 5. x is divided by 9, the
remainder is 3.
Look fora
counter
example
Leaves a
remainder of 3
when divided by
9.
Leaves a
remainder of 0
when divided by
6.
 x = 12
Leaves a
remainder of 5
when divided by
7.
Leaves a
remainder of 3
when divided by
9.
Leaves a
remainder of 3
when divided by
6.
 x = 75
Leaves a
remainder of 5
when divided by
7.
Eliminate
choice C as well
Counter
example exists
Statements
Together are
NOTsufficient
Questio Question Approac Statement Statement Combin Answ

52. What is the remainder when the positive integer x is divided
by 6?x is divided by 7, the remainder is 5. x is divided by 9, the
remainder is 3.
Look fora
counter
example
Leaves a
remainder of 3
when divided by
9.
Leaves a
remainder of 0
when divided by
6.
 x = 12
Leaves a
remainder of 5
when divided by
7.
Leaves a
remainder of 3
when divided by
9.
Leaves a
remainder of 3
when divided by
6.
 x = 75
Leaves a
remainder of 5
when divided by
7.
Eliminate
choice C as well
Answer choice E.
Counter
example exists
Statements
Together are
NOTsufficient
Questio Question Approac Statement Statement Combin Answ

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