How to subtract

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SSAT Upper Level Quantitative › How to subtract

Questions 1 - 10
1

Define a function as follows:

Evaluate .

Explanation

2

Define a function as follows:

Evaluate .

Explanation

3

and are prime integers. and . What is the greatest possible value of ?

Explanation

The greatest possible value of is the least possible value of subtracted from the greatest possible value of . The least prime between 55 and 65 is 59, and the greatest prime between 85 and 95 is 89, so and give the greatest possible value of , which is equal to

4

Define an operation as follows:

For all real numbers ,

.

Evaluate: .

Explanation

5

\dpi{100} 4.8-\frac{9}{2}

\dpi{100} 0.3

\dpi{100} -5.2

\dpi{100} \frac{5}{2}

\dpi{100} 2

Explanation

First convert \dpi{100} \frac{9}{2} into a decimal.

\dpi{100} 9\div 2=4\ remainder\ of\ 1

So we are left with \dpi{100} 4\frac{1}{2}, which is 4.5 in decimal form.

Now subtract:

\dpi{100} 4.8-4.5=0.3

6

and are prime integers. and .

How many possible values of are there?

Five

Six

Four

Seven

Eight

Explanation

The prime integers between 65 and 75 are 67, 71, and 73, so assumes one of those values; the prime integers between 45 and 55 are 47 and 53, so assumes one of those values. Therefore, one of the following holds true:

There are five possible values for (20 appears twice here).

7

\dpi{100} 4593-1296=

\dpi{100} 3297

\dpi{100} 3397

\dpi{100} 3497

\dpi{100} 497

Explanation

Subtract the two numbers, being careful not to forget to remove the borrowed number.

You can also add the solution back to 1296 to check your work, as addition is easier than subtraction.

\dpi{100} 1296+3297=4593

8

Define an operation as follows:

For all real numbers :

.

Evaluate .

The correct answer is not among the other responses.

Explanation

9

Define an operation on the real numbers as follows:

For all real numbers :

.

Evaluate .

The expression is undefined on the real numbers.

Explanation

However, is undefined in the real numbers; subsequently, so is .

10

Define a function as follows:

Evaluate .

The expression is undefined.

The correct answer is not among the other responses.

Explanation

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