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# The function f is defined by f (x) = 5x + 1 for all numbers

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The function f is defined by f (x) = 5x + 1 for all numbers [#permalink]  05 Mar 2017, 08:55
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Question Stats:

76% (00:43) correct 23% (00:57) wrong based on 60 sessions

The function $$f$$ is defined by $$f(x) = 5x + 1$$ for all numbers $$x$$.

 Quantity A Quantity B $$f(t + 54) - f(t + 50)$$ $$20$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: The function f is defined by f (x) = 5x + 1 for all numbers [#permalink]  11 Mar 2017, 17:09
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Explanation

Finding $$f (t + 54)$$:
$$f(x) = 5x + 1$$
$$f(t + 54) = 5(t + 54) + 1$$
$$f(t + 54) = 5t + 270 + 1$$
$$f (t + 54) = 5t + 271$$

Now finding $$f (t + 50)$$:

$$f(x) = 5x + 1$$
$$f (t + 50) = 5(t + 50) + 1$$
$$f (t + 50) = 5t + 250 + 1$$
$$f (t + 50) = 5t + 251$$

Now finding $$f (t + 54) - f (t + 50)$$:

$$f (t + 54) - f (t + 50)$$

$$=(5t + 271) - (5t + 251)$$

$$=(5t + 271) - 5t - 251$$
$$271 - 251 =20$$

The two quantities are equal. Hence option C is correct.
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Re: The function f is defined by f (x) = 5x + 1 for all numbers [#permalink]  10 Apr 2017, 10:42
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Carcass wrote:
The function f is defined by f (x) = 5x + 1 for all numbers x.

 Quantity A Quantity B f(t + 54) - f(t + 50) 20

Quantity A: f(t + 54) - f(t + 50)
Quantity B: 20

Let's find the values of f(t + 54) and f(t + 50)
When we plug t + 54 and t + 50 into the function we get:
f(t + 54) = 5(t + 54) + 1 = 5t + 270 + 1 = 5t + 271
f(t + 50) = 5(t + 50) + 1 = 5t + 250 + 1 = 5t + 251

So, we have:
Quantity A: [5t + 271]- [5t + 251]
Quantity B: 20

Simplify:
Quantity A: 20
Quantity B: 20

[Reveal] Spoiler:
C

Cheers,
Brent
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Re: The function f is defined by f (x) = 5x + 1 for all numbers [#permalink]  20 Apr 2017, 22:14
b is greater
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Re: The function f is defined by f (x) = 5x + 1 for all numbers [#permalink]  14 Nov 2018, 08:59
Tahir wrote:
b is greater

Correct Ans. C
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Re: The function f is defined by f (x) = 5x + 1 for all numbers [#permalink]  26 Nov 2018, 19:18

f(x) = 5x + 1

A: f(t + 54) - f(t + 50)
We substitute the input of functions instead of x:

f (t + 54) = 5 *(t+54) + 1 = 5t + 5*54 + 1
f (t + 50) = 5 *(t+50) + 1 = 5t + 5*50 + 1

A = f(t + 54) - f(t + 50) = 5t + 5*54 + 1 - (5t + 5*50 + 1) = 4*5 = 20

So A equals B and the answer is C.
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Re: The function f is defined by f (x) = 5x + 1 for all numbers   [#permalink] 26 Nov 2018, 19:18
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