Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 25 Sep 2018
Posts: 453
Location: United States (CA)
Concentration: Finance, Strategy
GPA: 3.97
WE: Investment Banking (Investment Banking)

If x, y, a, and b are positive integers less than 20, is the average
[#permalink]
Show Tags
27 Oct 2018, 22:31
Question Stats:
55% (02:27) correct 45% (01:50) wrong based on 53 sessions
HideShow timer Statistics
If x, y, a, and b are positive integers less than 20, is the average of x and y greater than the average of a and b? 1) x = 3a 2) The range of x and y> the range of a and b.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Why do we fall?...So we can learn to pick ourselves up again



NUS School Moderator
Joined: 18 Jul 2018
Posts: 1017
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)

If x, y, a, and b are positive integers less than 20, is the average
[#permalink]
Show Tags
28 Oct 2018, 04:58
Question whether \(\frac{x+y}{2} > \frac{a+b}{2}\) From statement 1:x = 3a. Clearly no info about y and b. Insufficient. From statement 2:
Range of x & y > Range of a & b. A range is just the difference between x and y or between a and b. If x = 3 and y = 5. and if a = 18 and b =19. Range of x&y > Range of a&b. But the average of x&y < a&b. If x = 19 and y = 17. and a = 3 and b = 2. Range of x&y > Range of a&b. And also the average of x&y > a&b. Insufficient. Combining also gives no extra info. E is the answer.
_________________
Press +1 Kudos If my post helps!



Intern
Joined: 29 Feb 2016
Posts: 3

Re: If x, y, a, and b are positive integers less than 20, is the average
[#permalink]
Show Tags
28 Oct 2018, 18:28
Wouldn't combining both A and B give us the required info to solve this question. It is given that (yx) > (ba) and x = 3a > y3a > ba > y> b+2a
for (y+x)/2 > (b+2a+3a)/2 > (y+x)/2 > (b+5a)/2 > (b+a)/2



NUS School Moderator
Joined: 18 Jul 2018
Posts: 1017
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)

Re: If x, y, a, and b are positive integers less than 20, is the average
[#permalink]
Show Tags
28 Oct 2018, 18:34
prabhath.y@gmail.com wrote: Wouldn't combining both A and B give us the required info to solve this question. It is given that (yx) > (ba) and x = 3a > y3a > ba > y> b+2a
for (y+x)/2 > (b+2a+3a)/2 > (y+x)/2 > (b+5a)/2 > (b+a)/2 Hi, The highlighted portion says that the range of x & y is greater than the range of a & b. Consider x as 6. y as 8. a as 17 and b as 18. Now yx = 2 > ba = 1. But Y>b+2a = 8>18+34. This is not true. Hope it helps.
_________________
Press +1 Kudos If my post helps!



Intern
Joined: 29 Feb 2016
Posts: 3

Re: If x, y, a, and b are positive integers less than 20, is the average
[#permalink]
Show Tags
28 Oct 2018, 19:19
the example that you have mentioned does not satisfy the constraint that x=3a. I was menntioning what would happen if we combine both the statements. Hope you can help.



Senior Manager
Joined: 25 Sep 2018
Posts: 453
Location: United States (CA)
Concentration: Finance, Strategy
GPA: 3.97
WE: Investment Banking (Investment Banking)

Re: If x, y, a, and b are positive integers less than 20, is the average
[#permalink]
Show Tags
28 Oct 2018, 23:10
Hi, prabhath.y@gmail.com maybe this helps you understand why both statements aren't sufficient. From statements one and two, we know that x = 3a and that the range of x and y > range of a and b. We can first determine the potential values for x and a. Because x, y, a, and b are all between zero and twenty, there are only a finite number of values for x and a. x = 3a a =1, x = 3 a = 2, x = 6 a = 3, x = 9 a = 4, x = 12 a = 5, x =15 a = 6, x =18 Using the values for a and x and the information from statement two, we can still create contradictory scenarios: Let a =1 and b = 5. The range will be 4, and the average will be 3. Let x = 3 and y = 8. The range will be 5, and the average will be 5.5. Average of a and b < Average of x and y Now let a = 6 and b = 19. The range will be 13, and the average will be 12.5. Let x = 18 and y = 1. The range will be 17, and the average will be 9.5. Average of a and b > Average of x and y Statements one and two together are not sufficient.
_________________
Why do we fall?...So we can learn to pick ourselves up again




Re: If x, y, a, and b are positive integers less than 20, is the average
[#permalink]
28 Oct 2018, 23:10






