SSAT Middle Level Quantitative - How to find the part from the whole with percentage

The product of two whole numbers is 12. Their difference could be

Explanation

The first thing to do is to determine what two numbers multiply to give you 12.

1 and 12

2 and 6

3 and 4

Now find the difference between each of those pairs.

The difference could be 1, 4, or 11. Only 4 is an answer choice.

What is of ?

Explanation

We can convert to $\frac{40}{100}$ or . We can then calculate $0.4\cdot 80=32$ .

What is 63% of 300 ?

Explanation

To find a percentage of a whole number, we will multiply the percentage by the whole number. So, we get

$63% \cdot 300$

$\frac{63}{100} \cdot 300$

$\frac{63}{100} \cdot \frac{300}{1}$

Now, the zeros can cancel out. So, we get

$\frac{63}{1} \cdot \frac{3}{1}$

$\frac{63 \cdot 3}{1 \cdot 1}$

$\frac{189}{1}$

Therefore, 63% of 300 is 189.

There are 1000 birds. 68% of the birds are green. How many birds are green?

$\textsl{\textsl{birds}}$

$720 \textsl{\textsl{ birds}}$

$68 \textup{\textsl{ birds}}$

$568 \textsl{\textsl{ birds}}$

Explanation

One way to solve this problem is to use cross multiplication. $68 % = \frac{68}{100}$

So in order to determine the number of green birds, set this proportion equal to $\frac{x}{1000}$ .

Therefore, $\frac{68}{100}= \frac{x}{1000}$

Cross multiply to get $100x=68\cdot1000$

. Now divide both sides of the equation by 100 to get

A faster way to solve this problem is to recognize that 100 and 1000 differ by only one decimal place (1000 has an extra zero). Therefore, in order to determine 68% of 1000, simply add an extra zero to 68 and you have 680 birds.

What is 250% of 750?

Explanation

Taking 250% of a number is the same as multiplying that number by 2.5. We therefore take the product:

$750 \cdot 2.5 = 1,875$

Susan has a coupon for 10% off any one item at her favorite department store. There is also a storewide sale of 50% off all purchases.

If Susan wants to by a shirt originally priced at $42, how much will she pay?

$18.90

$21.00

$37.80

$20.00

$16.50

Explanation

The storewide sale discounts the shirt by 50%:

$.5\times $42=$21$

Susan also has the 10% off coupon, so she's really paying 90% of the cost of the shirt:

$.9\times $21=$18.90$

70% of snacks served at a café are healthy while the rest of the snacks are unhealthy. There are 500 snacks. How many of these snacks are unhealthy?

$150 \textsl{ snacks}$

$225\textsl{ snacks}$

$350 \textsl{ snacks}$

$70 \textsl{ snacks}$

Explanation

First, we need to determine the percentage of snacks that are unhealthy. To do this, we subtract

Therefore, 30% of snacks are unhealthy.

The quick estimation method allows us to compute this problem quickly and save time on later questions. To begin, we need to determine 10% of the total amount of snacks. In order to find 10% of a number, simply move the decimal point one place to the left. So, 10% of 500 snacks is 50 snacks.

We want to determine how many snacks constitute 30% of the total amount of snacks. 30% is 3 times 10% so all we need to do is multiply 10% (50 snacks) by 3. Therefore,

$3\cdot50 \textsl{ snacks}=150 \textsl{ snacks}$ are unhealthy.

is what percent of ?

Explanation

In order to convert numbers to a percent, it is easiest to set up a ratio.

We know that percent is just per-cent or per-100, another way to write this is to divide the number by 100.

We would set up the ratio below with x being the number we are looking for:

$\frac{x}{100}=\frac{12}{25}$

Now we cross multiply 25 times x and 12 times 100 to get:

Dividing both sides by 25 will give us the percent.

$\frac{25x}{25}=\frac{1200}{25}$

On the left side the 25's will cancel to give us x, on the right side we may need to do some long division to eventually find that 1200/25 = 48.

Rectangle 1

Refer to the above figure, which is a rectangle divided into squares of equal size.

How many more squares must be shaded in if 60% of the entire rectangle is to be shaded in?

Explanation

The rectangle is divided into 20 squares; 60% of this is

$20 \times 60 % = 20 \times 0.60 = 12$ squares.

7 squares are already shaded in, so it is necessary to shade in

more squares.

Pie_graph

Refer to the above graph. If there were registered voters in Smith County in , how many voters were not registered as Republicans (nearest whole number)?