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# If b =3a, is the average (arithmetic mean) of the five terms in the li

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If b =3a, is the average (arithmetic mean) of the five terms in the li  [#permalink]

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23 Sep 2018, 23:08
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Difficulty:

35% (medium)

Question Stats:

72% (01:55) correct 28% (01:38) wrong based on 77 sessions

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3, 8, a, 17, b

If b =3a, is the average (arithmetic mean) of the five terms in the list above less than 8?

(1) a > 2
(2) a^2 < 9

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Re: If b =3a, is the average (arithmetic mean) of the five terms in the li  [#permalink]

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23 Sep 2018, 23:32
3, 8, a, 17, b

If b =3a, is the average (arithmetic mean) of the five terms in the list above less than 8?

(1) a > 2
(2) a^2 < 9

From statement 1: upon checking for a values >2 , we get NO @ a=3 and yes for all values @a>3 so not sufficient
from statement 2: a = +/-3 so answer would again be Yes and no

Combining both statments a= 3, we can say that avg mean of 5 no will not be >8 but exactly 8...

IMO C should be correct....
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Re: If b =3a, is the average (arithmetic mean) of the five terms in the li  [#permalink]

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23 Sep 2018, 23:37
Bunuel wrote:
3, 8, a, 17, b

If b =3a, is the average (arithmetic mean) of the five terms in the list above less than 8?

(1) a > 2
(2) a^2 < 9

+1 for B

$$(3+8+a+17+b)/5 < 8$$?
Given $$b = 3a$$
$$(3+8+17+4a)/5 < 8$$?
$$(28+4a) < 40$$?
$$4a < 12$$?
$$a < 3$$?

We need to find whether a < 3 ?

Statement 1:
$$a > 2$$
If $$a = 3$$ then Suff
If $$a = 2.5$$ then Insuff
Hence Statement 1 alone is Insuff

Statement 2:
$$a^2 < 9$$
$$|a| < 3$$
$$-3 < a < 3$$
All values of a will be less than 3. Hence Suff

Hence B
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If b =3a, is the average (arithmetic mean) of the five terms in the li  [#permalink]

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24 Sep 2018, 00:23
+1 for B,

Question stem basically asks us if the average of (3, 8, a, 17, 3a) is less than 8
On re-writing we get $$\frac{28+4a}{5}$$ < 8
$$28+4a < 40$$
$$4a<12$$
$$a<3$$

Statement 1 states a>2, which can mean a can take values 2.1, 2.5, 3, 3.5 etc. since question stem does not mention a to be an integer. Not sufficient.
Statement 2 states $$a^2 <9$$
which means that a is either less than 3 or -3, either way it will always be less than 3. Sufficient.
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Re: If b =3a, is the average (arithmetic mean) of the five terms in the li  [#permalink]

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24 Sep 2018, 00:52
Bunuel wrote:
3, 8, a, 17, b

If b =3a, is the average (arithmetic mean) of the five terms in the list above less than 8?

(1) a > 2
(2) a^2 < 9

From 1 , minimum value of a>2 .
i.e a+b=a+3a=4a>8
3+8+17+4a>36
avg >36/5 => avg>7 sufficient .

From 2 , different values are possible +/- 1 , +/-2 , +/-3 etc . for some values it is yes for others it is No . .

So answer is A . Please let me know if I am missing something . Thank you !!
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Re: If b =3a, is the average (arithmetic mean) of the five terms in the li  [#permalink]

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24 Sep 2018, 04:12
Bunuel wrote:
3, 8, a, 17, b

If b =3a, is the average (arithmetic mean) of the five terms in the list above less than 8?

(1) a > 2
(2) a^2 < 9

The question actually asks Is (28+4a)/5<8
Is a<3?
Statement 1: a>2
Clearly Insufficient. a=2.1 and a=4
Statement 2: a^2<9
(a-3)(a+3)<0
-3<a<3
Sufficient
B
Re: If b =3a, is the average (arithmetic mean) of the five terms in the li   [#permalink] 24 Sep 2018, 04:12
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