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# On six consecutive vocabulary quizzes, Kelvins lowest score was 70. Wa

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Joined: 22 Feb 2018
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On six consecutive vocabulary quizzes, Kelvins lowest score was 70. Wa  [#permalink]

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20 Aug 2018, 01:37
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Difficulty:

65% (hard)

Question Stats:

53% (01:58) correct 47% (02:15) wrong based on 46 sessions

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On six consecutive vocabulary quizzes, Kelvin's lowest score was 70. Was his average (arithmetic mean) quiz score for the six quizzes less than 80?

(1) The average of Kelvin's three lowest quiz scores was 72.
(2) The average of Kelvin's three highest quiz scores was 92.

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Re: On six consecutive vocabulary quizzes, Kelvins lowest score was 70. Wa  [#permalink]

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20 Aug 2018, 02:34
Princ wrote:
On six consecutive vocabulary quizzes, Kelvin's lowest score was 70. Was his average (arithmetic mean) quiz score for the six quizzes less than 80?

(1) The average of Kelvin's three lowest quiz scores was 72.
(2) The average of Kelvin's three highest quiz scores was 92.

Let the six scores are a,b,c,d,e, and f, a<b<c<d<e<f.
Given, a=70.
Question stem:- Is a+b+c+d+e+f < 80*6 ?
Or, Is 70+b+c+d+e+f < 480 ?
Or, Is b+c+d+e+f < 410?

St1:- The average of Kelvin's three lowest quiz scores was 72.
Or, $$\frac{a+b+c}{3}=72$$
Or, 70+b+c=72*3
Or, b+c=216-70=146
Now, possible values of b+c+d+e+f:
146+d+e+f=146+(>70)+(>70)+(>70)
So, (146+d+e+f) > 356
So, (b+c+d+e+f) may or mayn't be less than 410.
Insufficient.

St2:- The average of Kelvin's three highest quiz scores was 92.
Or, d+e+f=92*3=276
So, b+c+d+e+f =(>70)+(>70)+276, which is greater than 416.
Hence, b+c+d+e+f > 410
Sufficient.

Ans. (B)
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On six consecutive vocabulary quizzes, Kelvins lowest score was 70. Wa  [#permalink]

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20 Aug 2018, 03:28
Princ wrote:
On six consecutive vocabulary quizzes, Kelvin's lowest score was 70. Was his average (arithmetic mean) quiz score for the six quizzes less than 80?

(1) The average of Kelvin's three lowest quiz scores was 72.
(2) The average of Kelvin's three highest quiz scores was 92.

From the question stem, we can deduce the following information

1. Kevin's lowest vocabulary quiz score is 70.
2. Kevin wrote 6 tests - lowest possible total can be 70*6 = 420

We need to find out if the average was less than 80 (or) total is less than 480

When we individually analyze the first statement, we know that the sum of the three lowest
quiz scores is 72*3 = 216(where the lowest score is 70). Here, the minimum score possible
for the other two of the three quiz scores was $$\frac{216 - 70}{2} = 73$$.

If the other 3 scores are also 73, the total is 70+73*5 = 435. On the contrary, if the three
highest scores are 100 each, the total is 216+300 = 515. Therefore, the information that is
presented in the first statement is Insufficient

Now, if the three highest score average at 92, making the total 276, The minimum total for
the 3 lowest scores is 70*3 = 210. The minimum possible total is 486, which is greater than
480. Therefore, the information presented in the second statement is Sufficient - Option B
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On six consecutive vocabulary quizzes, Kelvins lowest score was 70. Wa   [#permalink] 20 Aug 2018, 03:28
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