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On a geography quiz, Emily and Katherine scored an average of 80 point

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Bunuel
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On a geography quiz, Emily and Katherine scored an average of 80 point [#permalink] New post   05 May 2019, 23:52
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On a geography quiz, Emily and Katherine scored an average of 80 points. If Katherine and Julia scored an average of 85 points,how many more points did Julia earn than Emily?

A. 15
B. 10
C. 7.5
D. 5
E. It cannot be determined from the information given.
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B
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Re: On a geography quiz, Emily and Katherine scored an average of 80 point [#permalink] New post   05 May 2019, 23:57
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Bunuel wrote:
On a geography quiz, Emily and Katherine scored an average of 80 points. If Katherine and Julia scored an average of 85 points,how many more points did Julia earn than Emily?

A. 15
B. 10
C. 7.5
D. 5
E. It cannot be determined from the information given.


Given \(\frac{K+E}{2}=80\) or, K+E=160 -----(1)
& \(\frac{K+J}{2}=85\) or K+J=170-----------(2)

On subtracting (1) from (2), we have

J-E=10
Or. J=E+10

Ans. (B)
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Re: On a geography quiz, Emily and Katherine scored an average of 80 point [#permalink] New post   06 May 2019, 00:19
We are asked J-E=?

E+K=160, E=160-K
J+K=170, J=170-K

J-E=170-k-(160-K)=10

IMO
Ans: B
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On a geography quiz, Emily and Katherine scored an average of 80 point [#permalink] New post   06 May 2019, 01:56
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They have given the avg points of E&K, K&J as 80 and 85
Therefore,

(E+K)/2 = 80 -- eq 1
(K+J)/2 =85 -- eq 2

==> (eq 2)-(eq 1) = (J-E)/2 = 5

==> J-E = 10

==> J=E+10

which implies that J has earned 10 points more than E

So the answer is option B
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On a geography quiz, Emily and Katherine scored an average of 80 point [#permalink]
06 May 2019, 01:56
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