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Math Expert V
Joined: 02 Sep 2009
Posts: 60628
For all nonnegative integers a, b, and c, the function G is defined by  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 52% (02:42) correct 48% (03:01) wrong based on 166 sessions

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For all nonnegative integers a, b, and c, the function G is defined by G(a,b,c)=7^2*a+7^1*b+7^0*c. Which of the following is equal to G(5,4,1)–G(3,6,4)?

A. G(0, 8, 1)
B. G(1, 4, 4)
C. G(1, 7, 7)
D. G(2, 2, 3)
E. G(3, 4, 2)

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Senior Manager  G
Joined: 24 Apr 2016
Posts: 313
Re: For all nonnegative integers a, b, and c, the function G is defined by  [#permalink]

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1
G(5,4,1)–G(3,6,4) = [49 *5 + 7*4 + 1] - [49*3 + 7*6 + 4] = [49*2 - 7*2 - 3] = 98 - 14 - 3 = 81

Out of the options given,

A. G(0, 8, 1) --> This adds up to 57, hence is rules out
B. G(1, 4, 4) -- > This adds up to 81
C. G(1, 7, 7) --> This is way more than 81
D. G(2, 2, 3) --> This is way more than 81
E. G(3, 4, 2) --> This is way more than 81

Answer is B. G(1, 4, 4)
Target Test Prep Representative G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2806
Re: For all nonnegative integers a, b, and c, the function G is defined by  [#permalink]

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1
Bunuel wrote:
For all nonnegative integers a, b, and c, the function G is defined by G(a,b,c)=7^2*a+7^1*b+7^0*c. Which of the following is equal to G(5,4,1)–G(3,6,4)?

A. G(0, 8, 1)
B. G(1, 4, 4)
C. G(1, 7, 7)
D. G(2, 2, 3)
E. G(3, 4, 2)

We are given that the function G is defined by G(a,b,c) = 7^2*a + 7^1*b + 7^0*c = 49a + 7b + c and need to determine which answer choice is equal to G(5,4,1) – G(3,6,4).

G(5,4,1) = 49(5) + 7(4) + 1 = 274

G(3,6,4) = 49(3) + 7(6) + 4 = 193

G(5,4,1) – G(3,6,4) = 274 – 193 = 81

Although we could go through each answer choice and see which one will yield the result of 81, an easier approach is to express 81 in the form of 49a + 7b + c. That is, if 81 = 49a + 7b + c, what are the values of a, b, and c? Keep in mind that a, b, and c are nonnegative integers.

81 = 49a + 7b + c

Since 81 is more than 49 but less than 2 times 49, a must be 1. In that case, we have:

81 = 49(1) + 7b + c

81 = 49 + 7b + c

32 = 7b + c

Since 32 is more than 4 times 7 but less than 5 times 7, b must be 4. In that case, we have:

32 = 7(4) + c

32 = 28 + c

4 = c

Therefore, a = 1, b = 4, and c = 4. In other words, 81 = 49(1) + 7(4) + 4.

However, 49(1) + 7(4) + 4 = G(1, 4, 4), so 81 = G(1, 4, 4).

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Manager  S
Joined: 03 Jan 2017
Posts: 132
Re: For all nonnegative integers a, b, and c, the function G is defined by  [#permalink]

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just keep calculating:
7^2 * 5 +7*\$+1 - 7^2*3+7*6+4=81
then try calculating; B is fine
Non-Human User Joined: 09 Sep 2013
Posts: 14003
Re: For all nonnegative integers a, b, and c, the function G is defined by  [#permalink]

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_________________ Re: For all nonnegative integers a, b, and c, the function G is defined by   [#permalink] 04 Dec 2019, 12:12
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