Abdulla wrote:If the average size of 3 accounts is $1 million, is the smallest account less than $500,000?

(1) The largest account is $1.3 million.
(2) One of the accounts is $0.7 million.


My question is if I changed statement one from 1.3 million to 1.2 million, A is going to be sufficient right?

a+b+c = 3 and a <= b<= c, is a < 0.5

Without any info, we can say that a <= 1 (the least can be at most the average).


(1) you say, c = 1.2
a + b = 1.8
a <= average
a <= 0.9M insufficient

IMO C

palvarez wrote:

Abdulla wrote:If the average size of 3 accounts is $1 million, is the smallest account less than $500,000?

(1) The largest account is $1.3 million.
(2) One of the accounts is $0.7 million.


My question is if I changed statement one from 1.3 million to 1.2 million, A is going to be sufficient right?

a+b+c = 3 and a <= b<= c, is a < 0.5

Without any info, we can say that a <= 1 (the least can be at most the average).


(1) you say, c = 1.2
a + b = 1.8
a <= average
a <= 0.9M insufficient

It's insufficient, you're right and your logic is very nice and clear, but what if a=.4M then b will be 1.4M which is larger than the largest number 1.3M (c), so we can't say a<=.9M
an if a= .5M
then b= 1.3M and c=1.3M too.
Thus, a<=.5M.... If the question was " is the smallest account less than or equal to $500,000"? then the first statement will be sufficient ..

Am I right ?

Abdulla,

Each choice is Insufficient, even if A says 1.2 mill, because the other accounts could be anything. try any numbers for each option and you will find that the smallest account could be > or < 500.00.

Try reading the latest article in the articles section, by Stacy; it is related to this. Also, search articles under "statistics" or "averages". Go for the more difficult average problems and concepts, then you won't be confused about this.

I am not sure what you are referring to as a and b in yyour last posting. If you are trying to alter the problem to see how the answer will differ, I suggest going to other average problems directly, because you will have better structured questions.

Abdulla wrote:

palvarez wrote:

Abdulla wrote:If the average size of 3 accounts is $1 million, is the smallest account less than $500,000?

(1) The largest account is $1.3 million.
(2) One of the accounts is $0.7 million.


My question is if I changed statement one from 1.3 million to 1.2 million, A is going to be sufficient right?

a+b+c = 3 and a <= b<= c, is a < 0.5

Without any info, we can say that a <= 1 (the least can be at most the average).


(1) you say, c = 1.2
a + b = 1.8
a <= average
a <= 0.9M insufficient

It's insufficient, you're right and your logic is very nice and clear, but what if a=.4M then b will be 1.4M which is larger than the largest number 1.3M (c), so we can't say a<=.9M
an if a= .5M
then b= 1.3M and c=1.3M too.
Thus, a<=.5M.... If the question was " is the smallest account less than or equal to $500,000"? then the first statement will be sufficient ..

Am I right ?

You made me thinking.

Let me refocus on the question.

a + b = 1.8 and c = 1.2
a <= 0.9 (max)
a = 1.8 -1.2 = 0.6 thats min, since we know b's max.
0.6 <= a <= 0.8

Sufficient.

heshamelaziry wrote:Abdulla,

Each choice is Insufficient, even if A says 1.2 mill, because the other accounts could be anything. try any numbers for each option and you will find that the smallest account could be > or < 500.00.

Try reading the latest article in the articles section, by Stacy; it is related to this. Also, search articles under "statistics" or "averages". Go for the more difficult average problems and concepts, then you won't be confused about this.

I am not sure what you are referring to as a and b in yyour last posting. If you are trying to alter the problem to see how the answer will differ, I suggest going to other average problems directly, because you will have better structured questions.

Thanks Hesham, I will definitely follow your advice, but see palvarez's last post.
btw, I used a,b, and c to follow with the same variables that palvarez assign.

palvarez wrote:

Abdulla wrote:

palvarez wrote:

Abdulla wrote:If the average size of 3 accounts is $1 million, is the smallest account less than $500,000?

(1) The largest account is $1.3 million.
(2) One of the accounts is $0.7 million.


My question is if I changed statement one from 1.3 million to 1.2 million, A is going to be sufficient right?

a+b+c = 3 and a <= b<= c, is a < 0.5

Without any info, we can say that a <= 1 (the least can be at most the average).


(1) you say, c = 1.2
a + b = 1.8
a <= average
a <= 0.9M insufficient

It's insufficient, you're right and your logic is very nice and clear, but what if a=.4M then b will be 1.4M which is larger than the largest number 1.3M (c), so we can't say a<=.9M
an if a= .5M
then b= 1.3M and c=1.3M too.
Thus, a<=.5M.... If the question was " is the smallest account less than or equal to $500,000"? then the first statement will be sufficient ..

Am I right ?

You made me thinking.

Let me refocus on the question.

a + b = 1.8 and c = 1.2
a <= 0.9 (max)
a = 1.8 -1.2 = 0.6 thats min, since we know b's max.
0.6 <= a <= 0.8

Sufficient.

Thanks palvarez, I think you got my point.

Ok, I am lost. I don't understand where the 1.2 coming from if A) says 1.3. Could you guide me through each option the conventional way

The OA sited is C. Is this still holding ?

heshamelaziry wrote:Ok, I am lost. I don't understand where the 1.2 coming from if A) says 1.3. Could you guide me through each option the conventional way

Adbulla modified the problem to see whetehr (1) alone is sufficient.

heshamelaziry wrote:The OA sited is C. Is this still holding ?

Hesham, you're right the OA is C and based on the abovementioned question, C is the answer, but I was trying to find a way to make the first statement sufficient, so I made some changes on the first statement.
I've bolded the changes.

If the average size of 3 accounts is $1 million, is the smallest account less than $500,000?
(1) The largest account is $1.2 million.

now, based on that.. my thought was as follows:

lets assign a, b, and c for the three accounts so,

a + b + c = 3,000,000 and from statement 1 we know that c=1,200,000

so,
a + b = 1,800,000 . Now in order to minimize (a) we should maximize (b) ..

Since (b) should be less or equal to (c) then, we can maximize it only to 1,200,000.

a + 1,200,000 + 1,200,000 = 3,000,000

Therefore, a= 600,000 ---------- which is greater than 500,000.

Hence, A is Sufficient based on the new changes.

Got it Abdulla. Excellent manipulation to test your self on the subject. Some of the problems that test this subject are quite annoying. could check this out:

https://www.beatthegmat.com/min-max-t48068.html