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# For all nonnegative integers a, b, and c, the function G is defined by

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Math Expert
Joined: 02 Sep 2009
Posts: 52905
For all nonnegative integers a, b, and c, the function G is defined by  [#permalink]

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06 Mar 2017, 00:43
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Difficulty:

85% (hard)

Question Stats:

57% (02:42) correct 43% (03:12) wrong based on 150 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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Re: For all nonnegative integers a, b, and c, the function G is defined by  [#permalink]

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06 Mar 2017, 02:12
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)
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Affiliations: Target Test Prep
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Posts: 2827
Re: For all nonnegative integers a, b, and c, the function G is defined by  [#permalink]

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07 Mar 2017, 16:51
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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Joined: 03 Jan 2017
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Re: For all nonnegative integers a, b, and c, the function G is defined by  [#permalink]

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18 Mar 2017, 14:11
just keep calculating:
7^2 * 5 +7*\$+1 - 7^2*3+7*6+4=81
then try calculating; B is fine
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Posts: 9833
Re: For all nonnegative integers a, b, and c, the function G is defined by  [#permalink]

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31 Mar 2018, 09:28
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Re: For all nonnegative integers a, b, and c, the function G is defined by   [#permalink] 31 Mar 2018, 09:28
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