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GRE Subject Test: Math : Factorials

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Example Questions

Example Question #11 : Factorials

Evaluate: 14!

Possible Answers:

87178291200

355687428096000

39916800

6227020800

Correct answer:

87178291200

Explanation:

Step 1: Write 14! in multiplication form:

$14!=14\cdot13\cdot12\cdot11\cdot10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1$

Step 2: Multiply Out

14!=87178291200

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Example Question #12 : Combinational Analysis

Evaluate: $\frac {14!}{13!}$

Possible Answers:

183

Correct answer:

Explanation:

Step 1: Expand the numerator and denominator:

$\frac {14\cdot 13\cdot 12\cdot 11\cdot 10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}{13\cdot 12\cdot 11\cdot 10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}$

Step 2: Cross all numbers out that are common to both the numerator and denominator:

We are left with .

The value of $\frac {14!}{13!}=14$

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Example Question #61 : Other Topics

What is ?

Possible Answers:

720

Correct answer:

Explanation:

Step 1: Recall definition of factorial...

Factorial is a mathematical expression where you multiply by every number below it until I hit . To find each number, subtract from the previous number

Step 2: Write out

3!=3(3-1)(3-2)(1)=3(2)(1)=6(1)=6

3!=6

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Example Question #12 : Factorials

Evaluate:

Possible Answers:

120

3628800

5040

40320

Correct answer:

40320

Explanation:

Step 1: Evaluate
Factorial-Multiply the number in front of the exclamation point by every number below until I hit
8!=8*7*6*5*4*3*2*1=40320

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Example Question #13 : Factorials

Evaluate: 2!*3!*4!

Possible Answers:

179

273

256

288

Correct answer:

288

Explanation:

Step 1: Evaluate each factorial expression separately...

2!=2*1=2
3!=3*2*1=6
4!=4*3*2*1=24

Step 2: Take the evaluation of each expression and apply the operations in the problem:

So, we get 2*6*24=288

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Example Question #14 : Factorials

Evaluate: $3!^{2^{3!}}$

Possible Answers:

$6^{6^{6}}$

4^6

$6^{12}$

6^4

Correct answer:

$6^{12}$

Explanation:

Step 1: Apply the power rule (stacked) of exponents..

We get $3!^{2*3!}$

Step 2: Evaluate the exponent...

We get $3!^{2*6}=3!^{12}$

Step 3: Re-write the base:

Final answer: $6^{12}$

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Example Question #15 : Factorials

Evaluate: $\large 4(3!)$

Possible Answers:

$\large 6!$

$\large 24$

12!

Correct answer:

$\large 24$

Explanation:

Step 1: Evaluate the parentheses first

$\large (3!)=(3*2*1)=6$

Step 2: Multiply the outside by the final value in Step 1..

$\large 6(4)=24$

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Example Question #16 : Factorials

Evaluate: $\large 5!$

Possible Answers:

$\large 360$

$\large 120$

$\large 121$

$\large 720$

Correct answer:

$\large 120$

Explanation:

Step 1: Define Factorial

Factorial is a mathematical expression which you multiply the number in front of the exclamation point by every number below it until you hit 1..

Step 2: Evaluate $\large 5!$

$\large 5!=5(5-1)(5-2)(5-3)(5-4)$
$\large 5!=5*4*3*2*1=120$

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Example Question #67 : Other Topics

Evaluate:

7!-6(6!)

Possible Answers:

None of the other answers

720

480

120

432

Correct answer:

720

Explanation:

Evaluate $\large 7!$ :

$\large 7!=7\cdot 6\cdot5\cdot4\cdot3\cdot2\cdot1=5040$

Evaluate $\large 6(6!)$ :

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

Evaluate $\large 7!-6(6!)$ :

$\large 5040-4320=720$

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Example Question #17 : Factorials

Simplify the following expression:

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

Possible Answers:

132.0009

121

132

123.004

366

Correct answer:

132.0009

Explanation:

Recall that ! means factorial 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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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 #11 : Factorials

Example Question #12 : Combinational Analysis

Example Question #61 : Other Topics

Example Question #12 : Factorials

Example Question #13 : Factorials

Example Question #14 : Factorials

Example Question #15 : Factorials

Example Question #16 : Factorials

Example Question #67 : Other Topics

Example Question #17 : Factorials

All GRE Subject Test: Math Resources

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