ISEE Middle Level Quantitative Reasoning - How to find the whole from the part

Danny drives 70 miles per hour. How long will it take him to reach his grandfather's house 245 miles away.

Explanation

Divide $245 \div 70=3.5$ .

Answer: It will take Danny 3.5 hours to arrive to his grandfather's house.

150% of what number is 9,000?

Explanation

Taking 150% of a number is the same as multiplying that number by 1.5. We can find our number, therefore, by dividing 9,000 by 1.5:

$9,000 \div 1.5 = 6,000$

$2^{3}*6^{2}=$

Explanation

First, solve the exponents:

$2^{3}=8$

$6^{2}=36$

Then, solve the equation:

Claude bought a new game for $32 at 20% off its original price. What was the original price of the game?

Explanation

Since the game was 20% off, that means the game's value is currently 80% of the original price.

In order to figure out what the original price of the game was, you must set up a proportion:

$\tfrac{32}{x} = \tfrac{80}{100}$

The proportion is set up this way because the $32 Claude paid is equal to 80% of the price of the game, not 100%. The x stands for the unknown original price of the game. Next, cross multiply. The bottom number of each fraction should be multiplied by the top number.

The above will be your result. You then must solve for x. To do this, divide by 80 on each side of the equation.

The value of x is your answer.

60% of 3,000 is equal to 40% of what number?

Explanation

60% of 3,000 is equal to $0.6 \cdot3,000 = 1,800$ .

40% of an unknown number can be written as . Set these equal and solve for :

$0.4 N \div 0.4 = 1,800 \div 0.4$

40% of is 200

70% of is 350

Which is the greater quantity?

(a)

(b)

(a) and (b) are equal

(a) is greater

(b) is greater

It is impossible to tell from the information given

Explanation

Each statement can be written as a proportion, and solved for its variable by cross-multiplying. In each case, we replace as follows:

$\frac{ \textup{Part}}{\textrm{Whole}} = \frac{\textrm{Pct}}{100}$

(a) The percent is 40, the part is 200, and the whole is :

$\frac{200}{y} = \frac{40}{100}$

$40 \cdot y = 200 \cdot100$

$40 \cdot y = 20,000$

$40 \cdot y \div 40 = 20,000 \div 40$

(b) The percent is 70, the part is 350, and the whole is :

$\frac{350}{z} = \frac{70}{100}$

$70 \cdot z = 350 \cdot100$

$70 \cdot z = 35,0 00$

$70 \cdot z \div 70= 35,0 00 \div 70$

$\small 4\cdot \left ( 3\cdot 5 \right )\div \left ( 2+1 \right )=$

Explanation

To solve:

Follow Order of Operations "PEMDAS".

First, solve equations within parentheses:

$\small 4\cdot \small \left ( 15 \right ) \div \left ( 3 \right )=$

Then, solve the entire equation working from left to right as multiplication and division are interchangeable:

$\small \small 60\div 3= 20$

After a discount of 20%, a boom box costs $144.

Which is the greater quantity?

(a) The price of the boom box before the discount

(b) $172.80

(a) is greater

(b) is greater

(a) and (b) are equal

It is impossible to tell from the information given

Explanation

Paying for something at 20% discount is the same as paying for it at 80% of the price.

If the boom box costs $172.80 before a 20% discount, then afterward, it costs 80% of this, or

$$172.80 \times 0.8 = $138.24 < $144.00$

Therefore, the original price must have been greater than $172.80.

is % of what number?

Round to the nearest thousandth.

Explanation

Remember that for percentages, the key to setting up the problem is intelligent translation. The word "is" becomes , "of" signals multiplication, "what" (and equivalent words) signal a variable ().