# GRE Practice Test - Problem Solving GRE Practice Test 1

Q. 1

1.If you join all the vertices of a heptagon, how many quadrilaterals will you get?

• A. 72
• B. 36
• C. 25
• D. 35
• E. 120

Q. 2

Four students have to be chosen 2 girls as the captain and vice-captain and 2 boys as captain and vice-captain of the school. There are 15 eligible girls and 12 eligible boys. In how many ways can they be chosen if Sunita is sure to be the captain?

• A. 114
• B. 1020
• C. 360
• D. 1848
• E. 1500

Q. 3

A teacher prepares a test. She gives 5 objective type questions out of which 4 have to be answered. Find the total ways in which they can be answered if the first 2 questions have 3 choices and the last 3 have 4 choices.

• A. 255
• B. 816
• C. 192
• D. 100
• E. 144

Q. 4

How many 5 digit numbers are there with distinct digits?

• A. 144
• B. 27216
• C. 4386
• D. 6432
• E. 720

Q. 5

In how many ways can 15 students be seated in a row such that the 2 most talkative children never sit together?

• A. 14!.14!
• B. 15.14!
• C. 14!
• D. 14! 13
• E. 15!

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Q. 6

In a school 5 colours are allotted to each house. If the flag of Tagore House has to be a sequence of three blocks of different colours, then how many flags can they choose from?

• A. 9
• B. 27
• C. 60
• D. 20
• E. 15

Q. 7

Find the number of words which can be formed by using the letters of the word EQUATION if each word has to start with a vowel.

• A. 40320
• B. 1260
• C. 1080
• D. 400
• E. 25200

Q. 8

How many five digit numbers can be formed using the digits 0, 2, 3,4and 5, when repetition is allowed such that the number formed is divisible by 2 or 5 or both?

• A. 100
• B. 150
• C. 3125
• D. 1500
• E. 125

Q. 9

A straight road runs from north to south. It has two turnings towards east and three turnings towards west. In how many ways can a person coming from east get on the road and go west?

• A. 2
• B. 3
• C. 9
• D. 6
• E. 5

Q. 10

How many heptagons can be drawn by joining the vertices of a polygon with 10 sides?

• A. 562
• B. 120
• C. 105
• D. 400
• E. 282

Q. 11

Four persons enter the lift of a seven storey building at the ground floor. In how many ways can they get out of the lift on any floor other than the ground floor?

• A. 720
• B. 1296
• C. 1663
• D. 360
• E. 2500

Q. 12

Ten different letters of an alphabet are given. 2 of these letters followed by 2 digits are used to number the products of a company. In haw many ways can the products be numbered?

• A. 52040
• B. 8100
• C. 5040
• D. 1000
• E. 4000

Q. 13

If P(2n+1,n-1):P(2n-1,n) = 3:5, find n.

• A. 2
• B. 4
• C. 6
• D. 8
• E. 10

Q. 14

A polygon has 20 diagonals. How many sides does it have?

• A. 12
• B. 11
• C. 10
• D. 9
• E. 8

Q. 15

A box contains 5 red and 4 blue balls. In how many ways can 4 balls be chosen such that there are at most 3 balls of each colour?

• A. 132
• B. 242
• C. 60
• D. 120
• E. 240