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If the average of 7 numbers is 72, how many of the numbers

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If the average of 7 numbers is 72, how many of the numbers [#permalink] New post 20 Mar 2012, 13:43
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If the average of 7 numbers is 72, how many of the numbers are equal to 72?

(1) Of the seven numbers, six are odd integers, and the average of those integers is 72.
(2) At least one of the numbers is equal to 72.
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Re: If the average of 7 numbers is 72, how many of the numbers [#permalink] New post 20 Mar 2012, 13:56
If the average of 7 numbers is 72, how many of the numbers are equal to 72?

(1) Of the seven numbers, six are odd integers, and the average of those integers is 72 --> since 6 out of 7 numbers are odd then none of them is equal to 72. Now, since the average of these 6 numbers is 72 then the 7th number must equal to 72 in order the overall average to be 72, which means that there are only one number equal to 72. Sufficient.

(2) At least one of the numbers is equal to 72. Not sufficient.

Answer: A.
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How many numbers are equivalent to 72? [#permalink] New post 01 Apr 2012, 10:43
If the average (arithmetic mean) of seven numbers is 72, how many of the numbers are equal to 72?

(1) Of the seven numbers, six are odd integers, and the average of those odd integers is 72.
(2) At least one of the numbers is equal to 72.
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Re: How many numbers are equivalent to 72? [#permalink] New post 01 Apr 2012, 11:26
Clearly (A).

Statement 1: If six of the seven integers are odd and their average is 72, it follows that the last (seventh) integer has to be 72 as well. Also, as the first six integers are odd, there is just one 72 in the set. Sufficient.

Statement 2: If one or more of the numbers is 72, the remaining numbers in the set can be a combination of less, more, or equal to 72. So we can have all 72s, or some more than 72 and some less, or some more than 72, some less, and some equal to 72. This makes the number of 72s uncertain. Insufficient.

Therefore (A)
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Re: How many numbers are equivalent to 72? [#permalink] New post 01 Apr 2012, 12:05
enigma123 wrote:
If the average (arithmetic mean) of seven numbers is 72, how many of the numbers are equal to 72?

(1) Of the seven numbers, six are odd integers, and the average of those odd integers is 72.
(2) At least one of the numbers is equal to 72.


Merging similar topics. Please ask if anything remains unclear.
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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!


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Re: How many numbers are equivalent to 72?   [#permalink] 01 Apr 2012, 12:05
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