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The function f(x) is defined as f(x+1) = f(x) + 5

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The function f(x) is defined as f(x+1) = f(x) + 5  [#permalink]

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New post 06 Feb 2019, 00:40
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C
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E

Difficulty:

  45% (medium)

Question Stats:

64% (02:24) correct 36% (03:00) wrong based on 50 sessions

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The function f(x) is defined as f(x+1) = f(x) + 5. If f(0) = 37, what is the sum of f(3) + f(4) +.... f(10)?

A. 476
B. 516
C. 556
D. 596
E. 636

Source: Experts Global

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Re: The function f(x) is defined as f(x+1) = f(x) + 5  [#permalink]

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New post 06 Feb 2019, 01:24
f(x+1) = f(x)+5
put x = 0, then
f(1) = f(0)+5
f(1) = 42
Similarly f(2) = 42+5 = 47; f(3) = 47+5 = 52.
Its an AP series, with a as 52 and d as 5.
n = 8.
\(S_8 = \frac{n}{2}[2a+(n-1)d]\)
\(S_8 = 4[104+35]\)
\(S_8 = 4*139 = 556\)

C is the answer.
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The function f(x) is defined as f(x+1) = f(x) + 5  [#permalink]

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New post 18 Aug 2019, 09:56
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For those who don't know the formula (however, I encourage you to learn it by heart as it shows up in many GMAT problems):

f(0) = 0
f(1) = 42
f(2) = 47
f(3) = 52
keep adding up 5 to 52 until reaching f(10) and keep them on your paper like this

52
57
62
67
72
77
82
87 --- f(10)

and add up the unit digits to get 36 and the tenth digists to get 52

so solution is 52+3=55 (and put next to it the 6 of 36) ---> 556

OPTION C

Note this can be done under 2 minutes and GMAT is not always about knowing the best approach (as you will not always know it), but about being flexibe in approaches

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The function f(x) is defined as f(x+1) = f(x) + 5  [#permalink]

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New post 18 Aug 2019, 10:05
pushpitkc wrote:
The function f(x) is defined as f(x+1) = f(x) + 5. If f(0) = 37, what is the sum of f(3) + f(4) +.... f(10)?

A. 476
B. 516
C. 556
D. 596
E. 636

Source: Experts Global


Given: The function f(x) is defined as f(x+1) = f(x) + 5. If f(0) = 37

Asked: What is the sum of f(3) + f(4) +.... f(10)?

f(0) = 37
f(1) = f(0) + 5 = 37 + 5 = 42
f(2) = f(1) + 5 = 42 + 5 = 47
f(3) = f(2) + 5 = 47 + 5 = 52

S = f(3) + f(4) +.... f(10) is an arithmetic progression with a = 52 d=5 n=8
S = n/2 {2a + (n-1)d}
S = 8/2{2*52 + (8-1)5} = 4(104 + 7*5) = 4(104 + 35) = 4* 139 = 556

IMO C

Alternatively

f(0) = 37
f(1) = f(0) + 5 = 37 + 5 = 42
f(2) = f(1) + 5 = 42 + 5 = 47
f(3) = f(2) + 5 = 47 + 5 = 52

f(3) = 52
f(4) = 57
f(5) = 62
f(6) = 67
f(7) = 72
f(8) = 77
f(9) = 82
f(10) = 87

f(3) + f(4) +.... f(10) = (87 + 52)/2 *8 = 139*4 = 556

IMO C
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The function f(x) is defined as f(x+1) = f(x) + 5   [#permalink] 18 Aug 2019, 10:05
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