A total of 240 processed tuna cans were delivered to a sales outlet in

Question

A total of 240 processed tuna cans were delivered to a sales outlet in 12 lots. Thereafter, 2 more lots were added to the lots already delivered. Is the average (arithmetic mean) number of processed tuna cans per lot for all the 14 lots less than 19?

(1) Each of the 2 lots delivered later had more than 12 processed tuna cans.
(2) Each of the 2 lots delivered later had less than 18 processed tuna cans.

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Archit3110 · Answer

#1
Each of the 2 lots delivered later had more than 12 processed tuna cans.
240+13+13 ; ( least value 13) and tuna can be a distinct integer value only
so avg < 19 not possible 
sufficient
#2
Each of the 2 lots delivered later had less than 18 processed tuna cans.
its yes and no if < =12 and >=12
IMO A ; sufficient

gvij2017 · Answer

Each of the 2 lots delivered later had more than 12 processed tuna cans.
240+13+13 ; ( least value 13) and tuna can be a distinct integer value only

Here each lot >12 so each lot may contain 13 or 30, for instance. 
Therefore average can be <19 or >19.

Not sufficient. 
Please let me know if I am wrong. And also correct me.

Archit3110 · Answer

gvij2017 
the question has asked  "Is the average (arithmetic mean) number of processed tuna cans per lot for all the 14 lots less than 19?" 
so it would be NO ; 
because for a total lot of 240 , the addition of 2 lots least 13 each will make the avg = (240+13+13)/14 = 19

Shwetabh54 · Answer

Lets work with the question first.

Is the (average of 14 lots) < 19
=> Is (Sum of 14 lots)/14 < 19
=> Is (Sum of 14 lots) < 19*14
=> Is Sum of 14 lots < 266

We know that sum of 12 lots is 240. Put that info in above equation

Is 240 + sum of last two lot < 266
=> Is sum of last two lot < 266 - 240
=> Is sum of last two lot < 26 .... equation 1

Now move to options :

1. Each last lot has > 12 can
=> Each last lot has >= 13 cans (Since can count must be integer) (>= is Sign for greater than and equal to)
=> Sum of Last two cans >= 26 cans

Now this is a Yes/No question type. Clearly sum of two last cans is greater than or equal to 26. Hence we will get a definite No for equation 1.
So, 1 is sufficient.

2. Each last lot has < 18 can
=> Sum of Last two cans < 36 cans
So, sum of last two cans count may be 10 and may be 30. For 10, we will get a "Yes" A and for 30 we will get a "No" against equation 1.
Hence, statement 2 is not sufficient.

Answer - A

A total of 240 processed tuna cans were delivered to a sales outlet in

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GMAT Data Sufficiency (DS) Questions

A total of 240 processed tuna cans were delivered to a sales outlet in

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