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Test: Combinations - GMAT MCQ


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10 Questions MCQ Test Practice Questions for GMAT - Test: Combinations

Test: Combinations for GMAT 2024 is part of Practice Questions for GMAT preparation. The Test: Combinations questions and answers have been prepared according to the GMAT exam syllabus.The Test: Combinations MCQs are made for GMAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Combinations below.
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Test: Combinations - Question 1

A firm has 4 senior partners and 6 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner. (Two groups are considered different if at least one group member is different)

Test: Combinations - Question 2

From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?

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Test: Combinations - Question 3

If two integers x and y such x>y are selected at random between -8 and 11, inclusive, how many cases are possible?

Test: Combinations - Question 4

A palindrome is a number that reads the same forward and backward. For example - 1331. How many 4-digit palindromes can be formed using two of the five digits - 1, 3, 5, 7, and 9?

Test: Combinations - Question 5

How many 5 digit numbers have at least one zero digit?

Test: Combinations - Question 6

How many arrangements of the letters A, C, C, E, N, T include at least one letter between the two C’s?

Test: Combinations - Question 7

A box contains 90 balls of different colours: 13 yellow, 19 green, 27 red, 10 black, 7 brown and 14 white. Find the smallest number V such that any V balls drawn from the box will contain at least 14 balls of the same colour.

Test: Combinations - Question 8

Warren has five vehicles: a blue convertible, a black sedan, a red coupe, a silver station wagon, and a blue SUV. If he drives a different car to work each day from Monday through Friday, in how many orders could he drive his five cars during a week if he always drives the convertible on Friday and won’t drive the same color vehicle on consecutive days?

Detailed Solution for Test: Combinations - Question 8

Restrictions:
1. He always drives the convertible on Friday
2. Won’t drive the same color vehicle on consecutive days -> He will not drive the blue SUV on Thursday, as on Friday he always drives the Blue Convertible.

Based on the above restrictions, below are the options what he can drive on each day.

This is a perfect scenario to use the total arrangements minus bad arrangements approach.

First, find the total, given that the blue convertible is on Friday: 4 * 3 * 2 * 1 * 1 = 24.

 Next, let’s find the number of arrangements where the blue convertible is on Friday and the blue SUV is on Thursday, violating the second restriction: 3 * 2 * 1 * 1 * 1 = 6. Good = Total - Bad = 24 - 6 = 18.

Alternatively you can look at the number of allowable options on each day, in which case it's helpful to flip the week and think Friday through Monday since your main constraints are on Friday (has to be the convertible) and on Thursday (can't be the blue SUV since he's already driving the blue convertible the next day). This means that you have:

1 option Friday, 3 options Thursday (anything but the two blue cars), 3 options Wednesday (he's already slotted in the convertible and one other car for Friday/Thursday, but now the blue SUV is back in the pool), 2 options Tuesday (anything but the three cars already slotted), and 1 option Monday (whatever's left).
So that calculation is 1 * 3 * 3 * 2 * 1 = 18.

Test: Combinations - Question 9

If the Board of Selectmen contains 4 positions, and if in the current election two candidates are running for each position, then in how many different ways can these candidates be elected to the Board?

Test: Combinations - Question 10

How many diagonals does a regular 11-sided polygon contain?

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