On six consecutive vocabulary quizzes, Kelvin's lowest score was 70.

Question

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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GMATinsight · Answer

Question: Is average of 6 quizzes < 80

Let, Quizzes score are a < b < c < d < e < f i.e. a = 70

Question: Is a+b+c+d+e+F < 480?

Question: Is b+c+d+e+F < 410?

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

i.e. 70 + b + c = 72*3
i.e. b+c = 146
Other quiz score are unknown hence

NOT SUFFICIENT

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

d+e+f = 92*3 = 276
i.e. Question is b+c+d+e+F < 410
i.e. Question is b+c+276 < 410
i.e. Question is b+c < 134

But since the lowes a = 70
so b+c must be greater than 70+70 = 140

i.e. b+c can NOT be less than 134 hence answer to the question is definitely NO

SUFFICIENT

Answer: Option B

gvij2017 · Answer

Given lowest score is 70 for six quizzes. 
Is avg< 80?

St. 1 avg for three lowest is 72. Now we can't tell about avg of six quizzes as we don't know about three other scores. Suppose each is 80 than NO. if each is 100 than YES.

St. 2 Avg of three highest is 92. Here we can assume that min sum of scores is 70+70+70+92*3 so the average is 486/6> 80
Sufficient.

B is answer.

Enchanting · Answer

Solution:
 • Minimum score = 70 
Statement 1: The average of three lowest quiz scores was 72.
 • Sum of the score three lowest quiz=  72*3 = 216 
• Sum of the score of second and third lowest quiz =  216-70 = 146 
o We cannot infer anything about the average of Kevin’s score
  Not sufficient.  
Statement 2: The average of three highest quiz score was 92.
 • Sum of score of highest three quizzes =  92*3 = 276 
 o Lowest score + 3 highest score =  276 + 70 = 346  
• Now, 2 subjects left
 o Minimum possible score is 70
o Let the score in those two subjects be 70 each.
o Sum of total score ≥  346 + 70 + 70 = 486 
  Average ≥ \frac{486}{6} 
 Average ≥  81  
o Thus, the minimum average of the score is 81.
  Average is not 80   
Answer:  Option B.

Archit3110 · Answer

lowest score = 70
is total score <480
#1
avg of lowest three scores = 72 ; 72*3 ; 216 so of other two low scores ; 216-70 ; 146 i.e 72,73
but other three scores not know insufficient
#2
The average of Kelvin's three highest quiz scores was 92.
i.e total highest = 92*3 ; 276
for other 3 scores lowest is 70 ; considering all to be same we get total score
276+210 ; 486 which is >480
so sufficient
OPTION B correct

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On six consecutive vocabulary quizzes, Kelvin's lowest score was 70.

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GMAT Data Sufficiency (DS) Questions

On six consecutive vocabulary quizzes, Kelvin's lowest score was 70.

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