ACT Math : How to divide odd numbers

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : Integers

Choose the answer which best solves the equation below:

\(\displaystyle 13 \cdot x = 351\)

Possible Answers:

\(\displaystyle x = 27\)

\(\displaystyle {}x=22\)

\(\displaystyle x=24\)

\(\displaystyle x=26\)

\(\displaystyle x=32\)

Correct answer:

\(\displaystyle x = 27\)

Explanation:

There are two ways to solve this problem. First you can do so algebraically by dividing both sides by 13:

\(\displaystyle \frac{351}{13} = x\)

\(\displaystyle x = 27\)

But, there is another way, which if you understand odd numbers, is even faster. Of all the answers above, only one is odd. You know, given the equation, that \(\displaystyle x\) must be odd--any odd number multiplied by an odd number will yeild an odd number.  If you multiply an odd number by an even number, you will get an even number. 

Example Question #1 : Even / Odd Numbers

Solve for \(\displaystyle x\) in the following equation:

\(\displaystyle 17x=493\)

Possible Answers:

\(\displaystyle 32\)

\(\displaystyle 26\)

\(\displaystyle 29\)

\(\displaystyle 28\)

Correct answer:

\(\displaystyle 29\)

Explanation:

There are two ways to approach this problem:

1. Use the rule that states that any two odd numbers multiplied together will yield another odd number. 

Using this rule, only one answer is an odd number (29) which will yield another odd number (493) when multiplied by the given odd number (17).

2. Solve algebraically:

\(\displaystyle 17x=493\)

\(\displaystyle \frac{493}{17}=29=x\)

Example Question #1 : Integers

Solve for \(\displaystyle x\) in the follwing equation:

\(\displaystyle 91x=7,735\)

Possible Answers:

\(\displaystyle 86\)

\(\displaystyle 88\)

\(\displaystyle 85\)

\(\displaystyle 84\)

Correct answer:

\(\displaystyle 85\)

Explanation:

There are two ways to approach this problem:

1. Use the rule that states that any two odd numbers multiplied together will yield another odd number. 

Using this rule, only one answer is an odd number (85) which will yield another odd number (7,735) when multiplied by the given odd number (91).

2. Solve algebraically:

\(\displaystyle 91x=7,735\)

\(\displaystyle \frac{7,735}{91}=85=x\)

 

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