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# Is the average (arithmetic mean) of a and b less than 40?

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Math Expert
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Is the average (arithmetic mean) of a and b less than 40?  [#permalink]

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29 Sep 2015, 21:35
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90% (00:50) correct 10% (01:09) wrong based on 157 sessions

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Is the average (arithmetic mean) of a and b less than 40?

(1) The average (arithmetic mean) of 3a and 3b is 117.
(2) b = 5a

Kudos for a correct solution.

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Is the average (arithmetic mean) of a and b less than 40?  [#permalink]

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02 Oct 2015, 01:35
1
It has to be A

(3a+3b)/2=117
(a+b)/2=39

so first statement is sufficient.

from b
6a/2=3a now a can be anything from 1 to 100

so insufficient

+1Kudos if you like solution
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Re: Is the average (arithmetic mean) of a and b less than 40?  [#permalink]

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06 Oct 2015, 08:11
Bunuel wrote:
Is the average (arithmetic mean) of a and b less than 40?

(1) The average (arithmetic mean) of 3a and 3b is 117.
(2) b = 5a

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

Question Type: Yes/No. “is the average of a and b less than 40?”

Given information from the question stem: You’re dealing with averages. One helpful tool to use when asked about the average of a group of numbers is to use the formula “Average * number = total.” In this case if the average is 40 and there are two numbers (a and b), then the question is really asking is (A+B)/2 < 40 or is “A +B < 80.”

Statement 1: if the average of 3a and 3b is 117 this means that “3a + 3b = 234.” If you divide by sides by 3 then you get “a + b = 78.” This is sufficient to answer the question. “Yes, the average of a + b < 40.” This statement is sufficient. The correct answer is either A or D.

Note: It would not be necessary to actually determine the value for “a + b.” Once you know that you can divide both sides of the equation “3a + 3b = 234” by 3 and get a value for “a + b” then you do not need to actually make the calculation. Either the average will be less than 40 or it will not be, but in either case you will have a consistent answer.

Statement 2: This statement does not provide any fixed values for a or b and so it cannot be determined if the average of a + b will be less than 40. This statement is not sufficient.

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Re: Is the average (arithmetic mean) of a and b less than 40?  [#permalink]

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21 Dec 2016, 16:46
Nice Question
Here is my solution to this one =>

$$Mean = \frac{Sum}{#}$$
Hence a+b/2<40
So a+b<80

We need to check if the sum of a and b is less than 80 or not

Statement 1-->
3a+3b=2*117
Hence a+b=2*39 => 78

Sufficient => YES

Statement 2-->
5a=b
1,5=> YES
10000,50000=> NO

Hence Not sufficient

Hence A

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Re: Is the average (arithmetic mean) of a and b less than 40?  [#permalink]

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06 Aug 2017, 13:06
1
i don't understand why ST 2 is insufficient. the way i see it:

(2) b=5a. --> $$\frac{6a}{2}$$<40 --> 6a <80 --> a~13. OK, plug in now: b=5(13); b=65.
- now, what is a+b? ~13 +65 = ~78. which is clearly under 80.

where am i going wrong here?
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Re: Is the average (arithmetic mean) of a and b less than 40?  [#permalink]

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10 Oct 2017, 02:42
LakerFan24 wrote:
i don't understand why ST 2 is insufficient. the way i see it:

(2) b=5a. --> $$\frac{6a}{2}$$<40 --> 6a <80 --> a~13. OK, plug in now: b=5(13); b=65.
- now, what is a+b? ~13 +65 = ~78. which is clearly under 80.

where am i going wrong here?

i had the exact same doubt
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Re: Is the average (arithmetic mean) of a and b less than 40?  [#permalink]

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11 Oct 2017, 03:49
3a+3b = 117*2
a+b/2 = 117/3

A Sufficient
From B we cannot conclude the average So answer should be A
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Re: Is the average (arithmetic mean) of a and b less than 40?  [#permalink]

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12 Oct 2017, 18:19
Bunuel wrote:
Is the average (arithmetic mean) of a and b less than 40?

(1) The average (arithmetic mean) of 3a and 3b is 117.
(2) b = 5a

We need to determine whether (a + b)/2 < 40, i.e., whether a + b < 80.

Statement One Alone:

The average (arithmetic mean) of 3a and 3b is 117.

Thus:

(3a + 3b)/2 = 117

3a + 3b = 234

a + b = 78

Statement one alone is sufficient to answer the question.

Statement Two Alone:

b = 5a

Since we do not know the values of a or b, we cannot determine whether a + b is less than 80.

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Re: Is the average (arithmetic mean) of a and b less than 40? &nbs [#permalink] 12 Oct 2017, 18:19
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