Number Concepts and Operations

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SSAT Upper Level: Quantitative › Number Concepts and Operations

Questions 1 - 10

There are 500 students at the high school. There are only two menu options: chicken or fish. If 15% of students ordered fish, how many students ordered chicken?

$425\ students$

$75\ students$

$85\ students$

$450\ students$

$325\ students$

Explanation

If 15% of students ordered fish, then 85% of the students must have ordered chicken. Then multiply 85% or $.85\times 500 = 425$ .

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).

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

$\dpi{100} 0.3$

$\dpi{100} -5.2$

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

$\dpi{100} 2$

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:

$\dpi{100} 4.8-4.5=0.3$

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

Define an operation $\Upsilon$ as follows:

For all real numbers ,

$a \Upsilon b = a^{5} - b^{4}$ .

Evaluate: $\frac{1}{2}; \Upsilon; \frac{1}{2}$ .

$-\frac{1}{32}$

$\frac{1}{32}$

$-\frac{1}{16}$

$\frac{1}{16}$

Explanation

$a \Upsilon b = a^{5} - b^{4}$

$\frac{1}{2}; \Upsilon; \frac{1}{2} =\left ( \frac{1}{2} \right )^{5} - \left ( \frac {1}{2} \right )^{4}$

$= \frac{1}{32} - \frac{1}{16}$

$= \frac{1}{32} - \frac{2}{32}$

$= -\frac{1}{32}$

Define an operation $\forall$ as follows:

For all real numbers :

$a \forall b = a^{4} + \frac{1}{b^{4}}$ .

Evaluate $\frac{1}{2} \forall (-2 )$ .

$\frac{1}{8}$

$16\frac{1}{16}$

$-15\frac{15}{16}$

The correct answer is not among the other responses.

Explanation

$a \forall b = a^{4} + \frac{1}{b^{4}}$

$\frac{1}{2} \forall (-2 ) = \left (\frac{1}{2} \right )^{4} + \frac{1}{(-2)^{4}}= \frac{1}{16} + \frac{1}{16} = \frac{2}{16} = \frac{1}{8}$

Define a function as follows:

$g(x)=\left | x^{5}-x^{2}\right |$

Evaluate .

Explanation

$g(x)=\left | x^{5}-x^{2}\right |$

$g(2)=\left | 2^{5}-2^{2}\right | = \left | 32-4\right | = \left | 28\right | = 28$

$g(-2)=\left |( -2)^{5}-\left (-2 \right )^{2}\right | = \left | -32-4\right | = \left | -36\right | = 36$

Define a function as follows:

$f(x) = 10 - \sqrt[3]{x} - \sqrt[5]{x}$

Evaluate .

The expression is undefined.

The correct answer is not among the other responses.

Explanation

$f(x) = 10 - \sqrt[3]{x} - \sqrt[5]{x}$

$f(-1) = 10 - \sqrt[3]{-1} - \sqrt[5]{-1} = 10 - (-1)- (-1)= 10+1+1 = 12$

Define a function on the real numbers as follows:

$f(x) = 100 -\left ( \sqrt{x} - \sqrt[4]{x} \right )$

Evaluate .

The expression is undefined.

The correct answer is not among the other responses.

Explanation

$f(x) = 100 -\left ( \sqrt{x} - \sqrt[4]{x} \right )$

$f(-1) = 100 -\left ( \sqrt{-1} - \sqrt[4]{-1} \right )$

Since even-numbered roots of negative numbers are not defined for real-valued functions, the expression is undefined.

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

$\dpi{100} 0.3$

$\dpi{100} -5.2$

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

$\dpi{100} 2$

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:

$\dpi{100} 4.8-4.5=0.3$

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