GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 Oct 2019, 08:32

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Is b = 21? (1) The average (arithmetic mean) of a, b and 16 is 14.

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58465
Is b = 21? (1) The average (arithmetic mean) of a, b and 16 is 14.  [#permalink]

### Show Tags

07 Jan 2018, 23:13
00:00

Difficulty:

35% (medium)

Question Stats:

70% (01:21) correct 30% (01:03) wrong based on 63 sessions

### HideShow timer Statistics

Is b = 21?

(1) The average (arithmetic mean) of a, b and 16 is 14.
(2) a < 5

_________________
Retired Moderator
Joined: 22 Aug 2013
Posts: 1428
Location: India
Re: Is b = 21? (1) The average (arithmetic mean) of a, b and 16 is 14.  [#permalink]

### Show Tags

08 Jan 2018, 11:32
Bunuel wrote:
Is b = 21?

(1) The average (arithmetic mean) of a, b and 16 is 14.
(2) a < 5

(1) (a+b+16)/3 = 14 or a+b+16 = 42 Or a+b = 26. But nothing else given about a/b. So insufficient.

(2) a < 5. But nothing given about b,c. Insufficient.

Combining the two statements, a+b = 26. Now if a=5, then b will be 26-5 = 21. That means if a<5, then definitely b will be greater than 21. This means b cannot be 21. Gives us NO as an answer to the question. So Sufficient.

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8033
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Is b = 21? (1) The average (arithmetic mean) of a, b and 16 is 14.  [#permalink]

### Show Tags

11 Jan 2018, 11:54
Bunuel wrote:
Is b = 21?

(1) The average (arithmetic mean) of a, b and 16 is 14.
(2) a < 5

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 2 variables (a and b) and 0 equations,C is most likely to be the answer. So, we should consider 1) & 2) first.

Condition 1) & 2):
(a+b+16)/3 = 14
⇔ a + b + 16 = 42
⇔ a + b = 26
⇔ b = 26 - a

Since a < 5, we have b > 21, which implies b≠21.

They are sufficient by CMT (Common Mistake Type) 1, since "no" also an answer.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Re: Is b = 21? (1) The average (arithmetic mean) of a, b and 16 is 14.   [#permalink] 11 Jan 2018, 11:54
Display posts from previous: Sort by