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```
1. Which one of the following operations does the operator # represent: addition, subtraction, multiplication or division?
(1)For all S, 10 # S = S # 10
(2)For all S, 10S # 3S = 30S2
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Both statements together are sufficient to answer the question, but neither statement alone is sufficient.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
2. How is Mary related to Jack?
1)Peter, the husband of Mary's only sister Rosy is a doctor.
2)Jack is Peter's sister-in-law's husband.
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Both statements together are sufficient to answer the question, but neither statement alone is sufficient.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
3. In the figure above, is PQ parallel to RS?
1)Angle PRS and angle QSR are equal.
2)PR = QS
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Both statements together are sufficient to answer the question, but neither statement alone is sufficient.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
4. In a fair, a lady bought a purse and a pair of sandals. Which item did she buy at a lower price?
1)The lady bought the purse at a 15% discount.
2)She bought the sandals at a 25% discount.
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
5. Does Peter have more coins in his pocket than Sam?
1)Mary has more coins in her pocket than Sam.
2)Peter has less coins in his pocket than Mary.
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
6. What is the value of A, if A and B are two distinct integers and their difference is 50?
1)A is an even integer.
2)A < B
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
7. Which employee got a bigger salary raise in absolute terms?
1)Jack got a 10% raise.
2)Mark got a 25% raise.
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
8. If the average of the marks obtained by three students of a class is 75, are the minimum marks obtained less than 50?
1)The highest marks obtained are 90.
2)One student has scored more than 75 marks.
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
9. If x and y are both positive integers, how much greater is x than y?
Statement (1): x + y = 20
Statement (2): x = y2
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement is sufficient by itself to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
10. What is the area of the circle?
1)The radius of the circle is 5.
2)The circumference of the circle is 5??.
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
11. Students in a school speak only English or only French or both the languages. How many students speak only English?
1)1/5th of the students in the school speak both English and French.
2)200 students in the school speak only French.
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
12. Is w an integer?
1)3w is an odd number.
2)2w is an even number.
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
13. Suppose 7A + 8B = 11. What is the value of B?
1)A is prime.
2)B = -5A
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
14. Is P > 0?
Statement (1): P2 > 0
Statement (2): P3 > 0
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
15. Which company reported to be the largest exporter of cotton in the year 2002?
1)Company A reported that its cotton consumption in the year 2002 increased by 10%.
2)Company B reported that its cotton consumption in the year 2002 increased by 20%.
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
16. If p and q do not equal 0, is p/q an integer?
1)p is prime.
2)q is even.
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
17. In the figure above, what is the value of AC?
1)Angle CBA = 900
2)CB + BA = 14
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
18. What is the value of x?
1)x2=4
2)x<0
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
19. What is the duration of the solar eclipse?
1)A solar eclipse begins at 10:00 a.m. on Monday and ends at 10:00 a.m. on Sunday.
2)The solar eclipse is 6 days long.
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
20. What was the percentage decrease of a company's production between 1st December and 31st December 2008?
1)The production reduced by $2000 in value during December 2008.
2)The production reduced by 15% from 2nd December 2008 to 20th December 2008.
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
21. What is the value of P?
1)P2 - 1 = 0
2)P = (10)0
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
22. What is the fifth term in the sequence S?
1)The seventh term of S is 5.
2)The sixth term of S is four times the fifth, and the seventh term is eight times the sixth.
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
23. Three persons have a combined weight of 500 pounds. What is the weight of the heaviest person?
1)One person weighs 150 pounds.
2)One person weighs 250 pounds.
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
24. What percentage of the items inspected in a unit are defective?
(1)The total production of items in the unit is 300.
(2)The ratio of the defective items to the non defective items is 12:35.
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
25. How many marbles are kept in a container?
1)If 5 marbles are taken out from the container, the number of marbles remaining in the container will be less than 15.
2)If 8 more marbles are put into the container, the total number of marbles in the container will rise to more than 20.
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
26. What is the value of P?
1. P + 20 = 100
2. P3 = 45
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
27. In the triangle ABD, BD is a straight line. What is the measure of angle CAB?
1)x = 800
2)y = 400
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
28. What is the value of 3x2 + 2x - 1?
1) x2 + 2x = 0
2) x = -2
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
29. How many cows in a herd of 50 cattle are black?
1)There are 12 oxen in the herd.
2)Forty two percent of the animals are black.
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
30. What is the value of even integers?
(1)3 < a < 21
(2)3???a is also an even integer.
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
31. If P is a positive number, what is 30% of P?
(1)50% of (50 / P) is less than 10.
(2)10% of (50 x P) is 225.
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
32. Is xy > 0 ?
1)x/y < 0
2)x + y < 0
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
33. If P is a cube of an integer and is between 5 and 100, what is the value of P?
1)P is odd.
2)P is the square of an integer.
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
34. What is the sum of A, B and C?
(1)A, B and C are odd numbers.
(2)The average of A, B and C is 5.
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
35. Is A greater than 0?
1)A3 is less than 0.
2)10A = -10
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
36. How many people in a city go to the office by car?
1)The total population of the city is 125000.
2)The total number of people going to the office by bus and train is1/3rd of the total population.
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
37. Is a > b?
1)a/3 > b/3
2)-a + c < -b + c
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
38. Is the product of A and B smaller than 100?
1)The sum of A and B is smaller than 100.
2)Both the numbers are smaller than 10.
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.

```
39. What is the area of the square ABCD?
1)AB=10 yards
2)Diagonal BD = ???128
```

**Answers:**

• Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.

• Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.

• Either statement by itself is sufficient to answer the question.

• Even both the statements together are not sufficient to answer the question.