# Deductive Reasoning Quiz Set 007

### Question 1

1. All rational numbers are integers, but not vice versa.
2. All integers are irrational numbers, but not vice versa.
3. √2 is an integer.

If the first two statements are true, the third statement is:

A

true.

B

false.

C

uncertain.

D

None.

Soln.
Ans: c

√2 is an irrational number, which is a known fact. On the basis of the truth of the first two statements, we have to test: "Is an irrational an integer?" If you try to draw a Venn diagram you will get three concentric circles. Rational inside Integer and the Integer inside Irrational, which means that there are some irrationals that are integers, and some that are not. Hence the answer should be "uncertain".

### Question 2

1. All the trees in the park are brown trees.
2. Some of the trees in the park are green.
3. All green in the park are brown trees.

If the first two statements are true, the third statement is.

A

true.

B

false.

C

uncertain.

D

none.

Soln.
Ans: a

All of the trees in the park are brown trees, so all green in the park are brown trees.

First statement gives: All are brown. The second says some are green, so all green have to be brown.

### Question 3

1. A torch is useful.
2. Useful things are costly.
3. A torch is costly.

If the first two statements are true, the third statement is.

A

true.

B

false.

C

uncertain.

D

none.

Soln.
Ans: a

Since torch is useful, it should be costly.

### Question 4

1. Three pens cost the same as two scales.
2. Four scales cost the same as one box.
3. Pens are more expensive than boxes.

If the first two statements are true, the third statement is.

A

true.

B

false.

C

uncertain.

D

none.

Soln.
Ans: b

Boxes are the most expensive item.

3P = 2S, 4S = B, so B is also = 2 x 3P = 6P.

### Question 5

1. Pencils cost more than blade.
2. Pencils cost less than pen.
3. Pen cost more than blade and pencils.

If the first two statements are true, the third statement is.

A

true.

B

false.

C

uncertain.

D

none.

Soln.
Ans: a

Because the first two statements are true, pen are the most expensive of the three. 