Todd recently competed in a dance contest. The contest had exactly 4 j

Question

Todd recently competed in a dance contest. The contest had exactly 4 judges, each of whom gave Todd an integer rating from 1 to 10. Todd received a mean rating of 7.5. Did any judge give Todd a rating of 10?

(1) One judge gave Todd a rating of 2
(2) Each of 3 judges gave Todd ratings of 8 or higher.

(1) One judge gave Todd a rating of 2
(2) Each of 3 judges gave Todd ratings of 8 or higher.

Bunuel · Accepted Answer

Todd recently competed in a dance contest. The contest had exactly 4 judges, each of whom gave Todd an integer rating from 1 to 10. Todd received a mean rating of 7.5. Did any judge give Todd a rating of 10?

(1) One judge gave Todd a rating of 2
(2) Each of 3 judges gave Todd ratings of 8 or higher.

Given a mean rating of 7.5 with 4 judges, Todd's total score must have been 30 points.

(1) One judge gave Todd a rating of 2

This implies that the remaining three judges gave Todd a total of 28 points. Since 3*9 = 27, which is less than 28, at least one judge must have given him a 10. Sufficient.

(2) Each of 3 judges gave Todd ratings of 8 or higher.

The above is clearly insufficient.

Answer: A.

Hope it's clear.

woodtm26 · Answer

From the stem:

a-d represent judge scores

Average = sum/# —> 7.5 = sum / 4 —> sum = 30
Sum = a+b+c+d

Statement 1)
Let’s say Judge A gave the score of 2 so you subtract 2 from the sum so sum = 28.

For remaining judges to total a sum of 28 at least one judge must be greater than 9 because 9*3=27; we need 28 because of the stem manipulation. Therefore at least one judge gives a score of 10.

Statement 2)
If 3 judges gave score of 8 then remaining judge will give score of 6 —> NO 10’s

If one judge gave score of 10 and remaining 3 scores were 8, 8, and 4 —> YES at least one 10

Since yes and no, S2 is NS

Posted from my mobile device

Oppenheimer1945 · Answer

Sum of rating=30

a+b+c+d=30

S1) a=2, b+c+d=28;
as 9+9+9=27, one rating has to be 10 (suff)

S2) Let (b,c,d)=(8,8,8), a=30-24=6
 Let (b,c,d)=(10,8,8), a=30-26=4 (can or cannot get a rating of 10)

(Not Suff)

A)

GMATinsight · Answer

Given:

Mean of ratings = 7.5
Number of ratings = Judges = 4
Total of 4 ratings = 7.5*4 = 30

Question: Did any judge gave rating 10?

Statement 1  : One judge gave rating = 2
i.e. sum of the other three ratings = 30-2 = 28

Sum of three ratings each less than or equal to 10 could be either {10, 9, 9} or {10, 10, 8}i.e. one of teh ratings is certainly 10 hence

SUFFICIENT

Statement 2  : Each of 3 judges gave Todd ratings of 8 or higher.
i.e. Ratings could be {10, 9, 9, 2} or {8, 8, 8, 6}
So judge may or may not have given rating to hence

NOT SUFFICIENT

Answer: Option A

Aboyhasnoname · Answer

In this question, Don't you think a statement like all the marks by judges carry an equal weight should have been there for a little more clarity? Only if we assume that all of the judges had equal weight we get the answer....

Bunuel bb what do you think?

Bunuel   bb  what do you think?

Bunuel · Answer

There’s no indication in the problem that the judges’ scores carry different weights, so the fair and natural assumption is that they are equally weighted.

Todd recently competed in a dance contest. The contest had exactly 4 j

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