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GRE Subject Test: Math : Factorials

Study concepts, example questions & explanations for GRE Subject Test: Math

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Example Questions

Example Question #1 : Factorials

Simplify the following expression:

$\frac{12!}{10!-4!}$

Possible Answers:

366

132.0009

132

123.004

121

Correct answer:

132.0009

Explanation:

Recall that ! means facotrial in math. This means we multiply the number by all positive integers less than itself. In other words, this...

$\frac{12!}{10!-4!}$

Becomes

$\frac{1\cdot 2\cdot3\cdot 4\cdot5\cdot6\cdot7\cdot8\cdot9\cdot10\cdot11\cdot12}{(1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9\cdot10)-(1\cdot2\cdot3\cdot 4)}$

This is a great job for a calculator, which yields:

132.0009

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Example Question #1 : Factorials

Evaluate: 5!-3(4!)

Possible Answers:

Correct answer:

Explanation:

Step 1: We need to define factorial (!). The operation (!) means that you multiply the number next to the ! by the next consecutive number down to 1.

Step 2: Expand the equation:

$5!=5\cdot4\cdot3\cdot2\cdot1=120$
3(4!)= $3(4\cdot 3\cdot 2\cdot 1)=3(24)=72$

Step 3: Evaluate the expression:

120-72=48

The answer to the expression is .

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Example Question #2 : Factorials

$\frac{5!}{3!-2!}$

Possible Answers:

Correct answer:

Explanation:

is the product of consecutive numbers 1 through

$\frac{5\times 4\times 3\times 2\times 1}{(3\times 2\times 1)-(2\times 1)} =$

$\frac{120}{6-2} = \frac{120}{4} = 30$

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Example Question #1 : Combinational Analysis

6! - 2(3!)

Possible Answers:

700

720

708

Correct answer:

708

Explanation:

is the product of consecutive numbers 1 through

$(6\times 5\times 4\times 3\times 2\times 1) - 2(3\times 2\times 1) =$

720 - 2(6) = 720 -12 = 708

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Example Question #4 : Factorials

Evaluate: $\frac {13!}{10!}$

Possible Answers:

1796

1776

1716

1736

Correct answer:

1716

Explanation:

Step 1: Rewrite the equation by using rule of factorials...

Rule of factorials: Multiply the number in front of factorial and each number one lower than the rest until I hit .

$\frac {13!}{10!}=\frac {13\cdot 12\cdot 11\cdot 10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}{10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}$

Step 2: Reduce any common numbers (colored in blue):

$\frac {13\cdot 12\cdot 11\cdot {\color{Blue} 10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}}{{\color{Blue} 10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}}$

We get $13\cdot12\cdot11$ !

Step 3: Evaluate what's left

$13\cdot12\cdot11=1716$

The value of the fraction is 1716 .

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Example Question #5 : Factorials

What is $_{8}P_{4}$ equal to?

Possible Answers:

1,600

1,580

1,640

1,680

Correct answer:

1,680

Explanation:

_nP_k depicts the permutation of n total objects with k objects being arranged.

Thus,

$_{8}P_{4} = \frac{n!}{k!}=\frac{8!}{4!}$

The upper factorial is the upper index, and the lower factorial is the difference of the indices.

$\frac{8!}{4!} = \frac{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{4\times 3\times 2\times 1}$

The or $4\times3\times2\times1$ will cancel out.

$8\times7\times6\times5 = 56\times30 = 1,680$

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Example Question #6 : Factorials

Twelve horses run a race. In how many ways can 3 horses finish in 1st, 2nd, and 3rd place, in any order?

Possible Answers:

225

230

220

200

Correct answer:

220

Explanation:

This particular question is asking one to find the combination. This is because the order of the 1st, 2nd, and 3rd place finishers is not important.

Thus evaluate $_{12}C_{3}$ .

$_{12}C_{3} = \frac{12!}{(12-3)! 3!}$

Because 12! and both consist of , the will cancel out leaving:

$\frac{12\times 11\times 10}{3\times 2\times 1}$

$\frac{12\times 11\times 10}{3\times 2\times 1} = \frac{1320}{6} = 220$

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Example Question #1 : Combinational Analysis

Evaluate: 10!-4(9!)+8!-3(7!)

Possible Answers:

3000000

2900000

2928250

2202480

Correct answer:

2202480

Explanation:

Step 1: Evaluate 10!

$10!=10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1=3628800$

Step 2: Evaluate 4(9!)

$4(9!)=4(9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1)=1451520$

Step 3: Evaluate

$8!=8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1=40320$

Step 4: Evaluate 3(7!)

$3(7!)=3(7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1)=15120$

Step 5: Add/Subtract values:

3628800-1451520+40320-15120=2202480

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Example Question #3 : Combinational Analysis

Evaluate: $3\cdot \bigg[\frac {9!}{7!}\bigg]$

Possible Answers:

216

225

289

243

Correct answer:

216

Explanation:

Step 1: Do the division of the factorials

$\bigg[\frac {9!}{7!}\bigg]=\frac {9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}{7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}$

Step 2: Simplify by cancelling out any terms on both top and bottom:

$\frac {9\cdot 8\cdot {\color{Blue} 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}}{{\color{Blue} 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}}=9\cdot8=72$

Step 3: Multiply the result of the division by 3..

$72 \cdot 3=216$

The value of that expression is 216 .

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Example Question #10 : Factorials

Evaluate: 7!-6(6!)

Possible Answers:

Correct answer:

Explanation:

Step 1: Find

$7!=7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1=5040$

Step 2: Find 6(6!)

$6(6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1)=6(720)=4320$

Step 3: Subtract the values from step 1 and step 2:

5040-4320=720=6!

The answer is

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GRE Subject Test: Math : Factorials

Study concepts, example questions & explanations for GRE Subject Test: Math

All GRE Subject Test: Math Resources

Example Questions

Example Question #1 : Factorials

Example Question #1 : Factorials

Example Question #2 : Factorials

Example Question #1 : Combinational Analysis

Example Question #4 : Factorials

Example Question #5 : Factorials

Example Question #6 : Factorials

Example Question #1 : Combinational Analysis

Example Question #3 : Combinational Analysis

Example Question #10 : Factorials

All GRE Subject Test: Math Resources

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