This one is a data sufficiency question and tests your understanding of positive and negative numbers. Basic number properties and inequalities. Is x > y ? Statement 1: x + y > x – y Statement 2: x + y < -(x + y)

1. GMAT QUANTITATIVE REASONING
INEQUALITIES &
NUMBER PROPERTIES
DATA SUFFICIENCY
Diagnostic Test

2. Question
Is x > y ?
Statement 1: x + y > x – y
Statement 2: x + y < -(x + y)

3. Step 1
Jot down answers to these 3 questions
before looking at the statements

4. Is x > y?
We will not even look at the statements while answering the following questions

5. Is x > y?
We will not even look at the statements while answering the following questions
When is the data sufficient?

6. Is x > y?
We will not even look at the statements while answering the following questions
When is the data sufficient?
It is an “is” question.

7. Is x > y?
We will not even look at the statements while answering the following questions
When is the data sufficient?
For any “is” question,
the data is sufficient
when we can answer the
question with a definite
yes or a definite no.
It is an “is” question.

8. Is x > y?
We will not even look at the statements while answering the following questions
When is the data sufficient? When is it an yes and when no?
For any “is” question,
the data is sufficient
when we can answer the
question with a definite
yes or a definite no.
It is an “is” question.

9. Is x > y?
We will not even look at the statements while answering the following questions
When is the data sufficient? When is it an yes and when no?
For any “is” question,
the data is sufficient
when we can answer the
question with a definite
yes or a definite no.
It is an “is” question. In this question, the answer
is yes when
x > y

10. Is x > y?
We will not even look at the statements while answering the following questions
When is the data sufficient? When is it an yes and when no?
For any “is” question,
the data is sufficient
when we can answer the
question with a definite
yes or a definite no.
It is an “is” question. In this question, the answer
is yes when
x > y
In this question, the answer
is no when
a. x < y or when
b. x = y

11. Is x > y?
We will not even look at the statements while answering the following questions
When is the data sufficient? When is it an yes and when no? What do we know about x & y?
For any “is” question,
the data is sufficient
when we can answer the
question with a definite
yes or a definite no.
It is an “is” question. In this question, the answer
is yes when
x > y
In this question, the answer
is no when
a. x < y or when
b. x = y

12. Is x > y?
We will not even look at the statements while answering the following questions
When is the data sufficient? When is it an yes and when no? What do we know about x & y?
For any “is” question,
the data is sufficient
when we can answer the
question with a definite
yes or a definite no.
It is an “is” question. In this question, the answer
is yes when
x > y
In this question, the answer
is no when
a. x < y or when
b. x = y
No additional information
is available about x and y.

13. Is x > y?
We will not even look at the statements while answering the following questions
When is the data sufficient? When is it an yes and when no? What do we know about x & y?
For any “is” question,
the data is sufficient
when we can answer the
question with a definite
yes or a definite no.
It is an “is” question. In this question, the answer
is yes when
x > y
In this question, the answer
is no when
a. x < y or when
b. x = y
No additional information
is available about x and y.
So, x and y belong to the set
of Real numbers.
They could both be positive,
negative, integers, fractions,
irrational.

14. Step 2
Let’s evaluate statement 1 alone

15. Is x > y?
Statement 1: x + y > x – y

16. Is x > y?
Statement 1: x + y > x – y
x + y > x – y

17. Is x > y?
Statement 1: x + y > x – y
x + y > x – y
i.e., 2y > 0 or y > 0

18. Is x > y?
Statement 1: x + y > x – y
x + y > x – y
i.e., 2y > 0 or y > 0
From the statement we can deduce that y is positive.

19. Is x > y?
Statement 1: x + y > x – y
x + y > x – y
i.e., 2y > 0 or y > 0
From the statement we can deduce that y is positive.
However, no information is available about x and its relation to y.

20. Is x > y?
Statement 1: x + y > x – y
x + y > x – y
i.e., 2y > 0 or y > 0
From the statement we can deduce that y is positive.
However, no information is available about x and its relation to y.
Hence, we will not be able to determine whether x > y.

21. Is x > y?
Statement 1: x + y > x – y
Statement 1 alone is NOT sufficient
x + y > x – y
i.e., 2y > 0 or y > 0
From the statement we can deduce that y is positive.
However, no information is available about x and its relation to y.
Hence, we will not be able to determine whether x > y.

22. Is x > y?
Statement 1: x + y > x – y
Eliminate choices A and D
Statement 1 alone is NOT sufficient
x + y > x – y
i.e., 2y > 0 or y > 0
From the statement we can deduce that y is positive.
However, no information is available about x and its relation to y.
Hence, we will not be able to determine whether x > y.

23. Is x > y?
Statement 1: x + y > x – y
Choices narrow down to B, C or E.
Eliminate choices A and D
Statement 1 alone is NOT sufficient
x + y > x – y
i.e., 2y > 0 or y > 0
From the statement we can deduce that y is positive.
However, no information is available about x and its relation to y.
Hence, we will not be able to determine whether x > y.

24. Step 3
Let’s evaluate statement 2 alone.

25. Is x > y?
Statement 2 : x + y < -(x + y)

26. Is x > y?
Statement 2 : x + y < -(x + y)
x + y < -(x + y)

27. Is x > y?
Statement 2 : x + y < -(x + y)
x + y < -(x + y)
i.e., 2(x + y) < 0 or x + y < 0

28. Is x > y?
Statement 2 : x + y < -(x + y)
x + y < -(x + y)
i.e., 2(x + y) < 0 or x + y < 0
If x + y < 0, what can we infer about x and y?

29. Is x > y?
Statement 2 : x + y < -(x + y)
x + y < -(x + y)
i.e., 2(x + y) < 0 or x + y < 0
If x + y < 0, what can we infer about x and y?
Possibility 1: Both x and y are negative

30. Is x > y?
Statement 2 : x + y < -(x + y)
x + y < -(x + y)
i.e., 2(x + y) < 0 or x + y < 0
If x + y < 0, what can we infer about x and y?
Possibility 1: Both x and y are negative
Possibility 2: One of x or y is positive and the other is negative

31. Is x > y?
Statement 2 : x + y < -(x + y)
x + y < -(x + y)
i.e., 2(x + y) < 0 or x + y < 0
If x + y < 0, what can we infer about x and y?
Possibility 1: Both x and y are negative
Possibility 2: One of x or y is positive and the other is negative
 What is the approach? Look for a counter example: Pick two sets of values satisfying the
condition in statement 2. If 1 set provides an answer yes and the other set provides a no, the
data is insufficient.

32. Is x > y?
Statement 2 : x + y < -(x + y). Simplifies as x + y < 0

33. Is x > y?
Statement 2 : x + y < -(x + y). Simplifies as x + y < 0
Both x and y are negative

34. Is x > y?
Statement 2 : x + y < -(x + y). Simplifies as x + y < 0
Both x and y are negative
Set 1: x = -2, y = -3. x + y = -5

35. Is x > y?
Statement 2 : x + y < -(x + y). Simplifies as x + y < 0
Both x and y are negative
Set 1: x = -2, y = -3. x + y = -5
Satisfies statement 2.

36. Is x > y?
Statement 2 : x + y < -(x + y). Simplifies as x + y < 0
Both x and y are negative
Set 1: x = -2, y = -3. x + y = -5
Satisfies statement 2.
Yes
x > y

37. Is x > y?
Statement 2 : x + y < -(x + y). Simplifies as x + y < 0
Both x and y are negative
Set 1: x = -2, y = -3. x + y = -5
Satisfies statement 2.
Set 2: x = -3, y = -2. x + y = -5
Yes
x > y

38. Is x > y?
Statement 2 : x + y < -(x + y). Simplifies as x + y < 0
Both x and y are negative
Set 1: x = -2, y = -3. x + y = -5
Satisfies statement 2.
Set 2: x = -3, y = -2. x + y = -5
This set also satisfies statement 2.
Yes
x > y

39. Is x > y?
Statement 2 : x + y < -(x + y). Simplifies as x + y < 0
Both x and y are negative
Set 1: x = -2, y = -3. x + y = -5
Satisfies statement 2.
Set 2: x = -3, y = -2. x + y = -5
This set also satisfies statement 2.
Yes
x > y
No
x < y

40. Is x > y?
Statement 2 : x + y < -(x + y). Simplifies as x + y < 0
Both x and y are negative
Statement 2 alone is also NOT sufficient
Set 1: x = -2, y = -3. x + y = -5
Satisfies statement 2.
Set 2: x = -3, y = -2. x + y = -5
This set also satisfies statement 2.
Yes
x > y
No
x < y

41. Is x > y?
Statement 2 : x + y < -(x + y). Simplifies as x + y < 0
Both x and y are negative
Eliminate choice B
Statement 2 alone is also NOT sufficient
Set 1: x = -2, y = -3. x + y = -5
Satisfies statement 2.
Set 2: x = -3, y = -2. x + y = -5
This set also satisfies statement 2.
Yes
x > y
No
x < y

42. Is x > y?
Statement 2 : x + y < -(x + y). Simplifies as x + y < 0
Both x and y are negative
Choices narrow down to C or E.
Eliminate choice B
Statement 2 alone is also NOT sufficient
Set 1: x = -2, y = -3. x + y = -5
Satisfies statement 2.
Set 2: x = -3, y = -2. x + y = -5
This set also satisfies statement 2.
Yes
x > y
No
x < y

43. Is x > y?
Statement 2 : x + y < -(x + y). Simplifies as x + y < 0
Both x and y are negative One positive and one negative.
Choices narrow down to C or E.
Eliminate choice B
Statement 2 alone is also NOT sufficient
Set 1: x = -2, y = -3. x + y = -5
Satisfies statement 2.
Set 2: x = -3, y = -2. x + y = -5
This set also satisfies statement 2.
Yes
x > y
No
x < y

44. Is x > y?
Statement 2 : x + y < -(x + y). Simplifies as x + y < 0
Both x and y are negative One positive and one negative.
Choices narrow down to C or E.
Eliminate choice B
Statement 2 alone is also NOT sufficient
Set 1: x = -2, y = -3. x + y = -5
Satisfies statement 2.
Set 2: x = -3, y = -2. x + y = -5
This set also satisfies statement 2.
Yes
x > y
No
x < y
Set 1: x = 2, y = -3. x + y = -1

45. Is x > y?
Statement 2 : x + y < -(x + y). Simplifies as x + y < 0
Both x and y are negative One positive and one negative.
Choices narrow down to C or E.
Eliminate choice B
Statement 2 alone is also NOT sufficient
Set 1: x = -2, y = -3. x + y = -5
Satisfies statement 2.
Set 2: x = -3, y = -2. x + y = -5
This set also satisfies statement 2.
Yes
x > y
No
x < y
Set 1: x = 2, y = -3. x + y = -1
Satisfies statement 2.

46. Is x > y?
Statement 2 : x + y < -(x + y). Simplifies as x + y < 0
Both x and y are negative One positive and one negative.
Choices narrow down to C or E.
Eliminate choice B
Statement 2 alone is also NOT sufficient
Set 1: x = -2, y = -3. x + y = -5
Satisfies statement 2.
Set 2: x = -3, y = -2. x + y = -5
This set also satisfies statement 2.
Yes
x > y
No
x < y
Set 1: x = 2, y = -3. x + y = -1
Satisfies statement 2.
Yes
x > y

47. Is x > y?
Statement 2 : x + y < -(x + y). Simplifies as x + y < 0
Both x and y are negative One positive and one negative.
Choices narrow down to C or E.
Eliminate choice B
Statement 2 alone is also NOT sufficient
Set 1: x = -2, y = -3. x + y = -5
Satisfies statement 2.
Set 2: x = -3, y = -2. x + y = -5
This set also satisfies statement 2.
Yes
x > y
No
x < y
Set 1: x = 2, y = -3. x + y = -1
Satisfies statement 2.
Yes
x > y
Set 2: x = -3, y = 2. x + y = -1

48. Is x > y?
Statement 2 : x + y < -(x + y). Simplifies as x + y < 0
Both x and y are negative One positive and one negative.
Choices narrow down to C or E.
Eliminate choice B
Statement 2 alone is also NOT sufficient
Set 1: x = -2, y = -3. x + y = -5
Satisfies statement 2.
Set 2: x = -3, y = -2. x + y = -5
This set also satisfies statement 2.
Yes
x > y
No
x < y
Set 1: x = 2, y = -3. x + y = -1
Satisfies statement 2.
Yes
x > y
Set 2: x = -3, y = 2. x + y = -1
This set also satisfies statement 2.

49. Is x > y?
Statement 2 : x + y < -(x + y). Simplifies as x + y < 0
Both x and y are negative One positive and one negative.
Choices narrow down to C or E.
Eliminate choice B
Statement 2 alone is also NOT sufficient
Set 1: x = -2, y = -3. x + y = -5
Satisfies statement 2.
Set 2: x = -3, y = -2. x + y = -5
This set also satisfies statement 2.
Yes
x > y
No
x < y
Set 1: x = 2, y = -3. x + y = -1
Satisfies statement 2.
Yes
x > y
Set 2: x = -3, y = 2. x + y = -1
This set also satisfies statement 2.
No
x < y

50. Is x > y?
Statement 2 : x + y < -(x + y). Simplifies as x + y < 0
Both x and y are negative One positive and one negative.
Choices narrow down to C or E.
Eliminate choice B
Statement 2 alone is also NOT sufficient
Set 1: x = -2, y = -3. x + y = -5
Satisfies statement 2.
Set 2: x = -3, y = -2. x + y = -5
This set also satisfies statement 2.
Yes
x > y
No
x < y
Set 1: x = 2, y = -3. x + y = -1
Satisfies statement 2.
Yes
x > y
Set 2: x = -3, y = 2. x + y = -1
This set also satisfies statement 2.
No
x < y
Evaluating one positive and one negative is NOT needed as we have already proved insufficiency when both x and y
are negative. We have done it only to illustrate how to evaluate such a case.

51. Step 4
Let’s combine data from both the
statements.

52. Is x > y?
Statements Together : x + y > x – y and x + y < -(x + y)

53. Is x > y?
Statements Together : x + y > x – y and x + y < -(x + y)
Gist of statement 1

54. Is x > y?
Statements Together : x + y > x – y and x + y < -(x + y)
Gist of statement 1
y > 0

55. Is x > y?
Statements Together : x + y > x – y and x + y < -(x + y)
Gist of statement 1 Gist of statement 2
y > 0

56. Is x > y?
Statements Together : x + y > x – y and x + y < -(x + y)
Gist of statement 1 Gist of statement 2
y > 0 x + y < 0

57. Is x > y?
Statements Together : x + y > x – y and x + y < -(x + y)
Gist of statement 1 Gist of statement 2 Taken together
y > 0 x + y < 0

58. Is x > y?
Statements Together : x + y > x – y and x + y < -(x + y)
Gist of statement 1 Gist of statement 2 Taken together
y > 0 x + y < 0 ‘y’ is positive

59. Is x > y?
Statements Together : x + y > x – y and x + y < -(x + y)
Gist of statement 1 Gist of statement 2 Taken together
y > 0 x + y < 0 ‘y’ is positive
x + y is negative

60. Is x > y?
Statements Together : x + y > x – y and x + y < -(x + y)
Gist of statement 1 Gist of statement 2 Taken together
y > 0 x + y < 0 ‘y’ is positive
x + y is negative
So, x has to be negative

61. Is x > y?
Statements Together : x + y > x – y and x + y < -(x + y)
Gist of statement 1 Gist of statement 2 Taken together
y > 0 x + y < 0 ‘y’ is positive
x + y is negative
So, x has to be negative
If y is positive and x is negative, x < y. Answer definite NO.

62. Is x > y?
Statements Together : x + y > x – y and x + y < -(x + y)
Gist of statement 1 Gist of statement 2 Taken together
Statements together are SUFFICIENT
y > 0 x + y < 0 ‘y’ is positive
x + y is negative
So, x has to be negative
If y is positive and x is negative, x < y. Answer definite NO.

63. Is x > y?
Statements Together : x + y > x – y and x + y < -(x + y)
Gist of statement 1 Gist of statement 2 Taken together
Eliminate choice E
Statements together are SUFFICIENT
y > 0 x + y < 0 ‘y’ is positive
x + y is negative
So, x has to be negative
If y is positive and x is negative, x < y. Answer definite NO.

64. Is x > y?
Statements Together : x + y > x – y and x + y < -(x + y)
Gist of statement 1 Gist of statement 2 Taken together
Answer is choice C
Eliminate choice E
Statements together are SUFFICIENT
y > 0 x + y < 0 ‘y’ is positive
x + y is negative
So, x has to be negative
If y is positive and x is negative, x < y. Answer definite NO.

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