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# If a certain company purchased computers at \$2000 each and printers \$

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If a certain company purchased computers at \$2000 each and printers \$ [#permalink]
VeritasPrepKarishma and other experts:
The answer is not B as the LCM of 2000 and 300 is less than 15,000. This is the reason the equation will not form a Diophantine equation and will not result in a unique solution.

I think my logic is sound. But can you pls comment on my logic and if I can use it reliably on similar questions, in which, it ultimately comes down to unicity or plurality of solution to an equation, without testing numbers? thanks
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Re: If a certain company purchased computers at \$2000 each and printers \$ [#permalink]
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NoHalfMeasures wrote:
VeritasPrepKarishma and other experts:
The answer is not B as the LCM of 2000 and 300 is less than 15,000. This is the reason the equation will not form a Diophantine equation and will not result in a unique solution.

I think my logic is sound. But can you pls comment on my logic and if I can use it reliably on similar questions, in which, it ultimately comes down to unicity or plurality of solution to an equation, without testing numbers? thanks

Dont know about the application of diophantine equation to other similar questions but this is how I would solve this question.

You are given that each computer costs 2000 while each printer costs 300. You need to find the # of computers = c.

Per statement 1, p>3. Clearly not sufficient.

Per statement 2, 2000c+300p=15000 ---> 20c+3p=150. Solution sets for (c,p) can be (6,10) or (3,30). Thus no unique solution. Not sufficient.

Combining the 2 statements, still the 2 solution sets above (6,10) or (3,30) are applicable and hence E is the correct answer as you do not get a unique solution for the number of computers.

Hope this helps.
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Re: If a certain company purchased computers at \$2000 each and printers \$ [#permalink]
Thanks for your reply Engr2012. However, I know how to solve it using conventional methods. Im more interested in conceptual understanding of my logic and its applicability to similar questions. thanks again
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Re: If a certain company purchased computers at \$2000 each and printers \$ [#permalink]
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If a certain company purchased computers at \$2000 each and printers \$300 each , how many computers did it purchase?

(1) More than three printers were purchased
(2) The total amount for the purchase of the computers and printers was \$15,000

When you modify the original condition and the question, it is frequently given on GMAT Math test which is "2 by 2" que.
Attachment:

GCDS sunita123 If a certain company purchased (20160119).jpg [ 25.83 KiB | Viewed 10996 times ]

On the table, there are 2 variables(a,b), which should match with the number of equations. So you need 2 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer. When 1) & 2), 2000a+200b=15000 -> 20a+3b=150 -> (a,b)=(3,30),(6,10), which is not unique and not sufficient. Therefore, the answer is E.

 For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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Re: If a certain company purchased computers at \$2000 each and printers \$ [#permalink]
Statement (1);

Statement (2):
From the stem we know that the total purchase of computers and printers can be expressed as:

2000c + 300p

From this statement, we know that sum will be \$15,000, so:

15000 = 2000c + 300p

This is a single expression with TWO variables so it is unlikely to give us a unique (integer) value for both of our variables, but we can see what pairs would work:

First we check the high priced item, Computers.

0 comp = 0 (15,000 left for printers = 50 printers)
1 comp = 2,000 (13,000 left for printers = NOT WHOLE # of printers)
2 comps = 4,000 (11,000 left for printers = NOT WHOLE # of printers)
3 comps = 6,000 (9,000 left for printers = 30 printers)
4 comps = 8,000 (7,000 left for printers = NOT WHOLE # of printers)
5 comps = 10,000 (5,000 left for printers = NOT WHOLE # of printers)
6 comps = 12,000 (3,000 left for printers = 10 printers)
7 comps = 14,000 (1,000 left for printers = NOT WHOLE # of printers)
8 comps = TOO MUCH

So statement (2) gives 3 possible outcomes:
- 0 computers and 50 printers
- 3 computers and 30 printers
- 6 computers and 10 printers

Statement (1+2)
We have not eliminated any of the possible scenarios from statement (1) because in ALL cases more than 3 printers were purchased.

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Re: If a certain company purchased computers at \$2000 each and printers \$ [#permalink]
this is still the problem in which we have one equation and 2 variable.
from 2
2000 c+ 300 p= 15000
20c + 3p =150
p= (150-20c)/3= 50-20c/3
c=3 and c=6

on og book, there is a problem in which there is only on value of c and only condition2 is good.
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Re: If a certain company purchased computers at \$2000 each and printers \$ [#permalink]
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sunita123 wrote:
If a certain company purchased computers at \$2000 each and printers \$300 each , how many computers did it purchase?

(1) More than three printers were purchased
(2) The total amount for the purchase of the computers and printers was \$15,000

Given: Company purchased computers at \$2,000 each and printers \$300 each

Target question: How many computers did it purchase?
When I SCAN the two statements, they both feel insufficient, AND I’m pretty sure I can identify some cases with conflicting answers to the target question. So, I’m going to head straight to……

Statements 1 and 2 combined
There are at least two scenarios that satisfy BOTH statements:
Case a: The company bought 10 printers (for a total cost of \$3000) and 6 computers (for a total cost of \$12,000). In this case, the answer to the target question is the company purchased 6 computers
Case b: The company bought 30 printers (for a total cost of \$9000) and 3 computers (for a total cost of \$6,000). In this case, the answer to the target question is the company purchased 3 computers
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Cheers,
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Re: If a certain company purchased computers at \$2000 each and printers \$ [#permalink]
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Re: If a certain company purchased computers at \$2000 each and printers \$ [#permalink]
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