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Re: Albert spent $100 in total on four different types of scratch tickets, [#permalink]
Celestial09 wrote:
Hi,
IMO it should be B
Though I tried to arrive by using number plugging system.
St 1 it could be 10 on G and 20 on C. this makes 30 and we know max was 40. this gives 10+20+40=70 and rest is 30
it could be 5 on g then 10 on c and we know 40 already spent. this gives 55 and rest is 45
so A is ruled out.

St 2. 20 on each atleast. we know 40 already spent. so 20 on rest three. this gives 20* 3 = 60 + 40 =100
So it should be B

Kudos if its a correct solution



Bunuel wrote:
Albert spent $100 in total on four different types of scratch tickets, and he did not spend more than $40 on any one type of scratch ticket. How much did he spend on the scratch ticket on which he spent the least?

(1) Albert spent twice as much on C-type tickets as he did on G-type tickets.
(2) Albert spent at least $20 on each type of ticket.


Kudos for a correct solution.



We didn't no that he already spent $40.
we know only that "he did not spend more than $40 on any one type"
so it can be $25 on each type of stickers.
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Re: Albert spent $100 in total on four different types of scratch tickets, [#permalink]
Bunuel wrote:
Albert spent $100 in total on four different types of scratch tickets, and he did not spend more than $40 on any one type of scratch ticket. How much did he spend on the scratch ticket on which he spent the least?

(1) Albert spent twice as much on C-type tickets as he did on G-type tickets.
(2) Albert spent at least $20 on each type of ticket.


Kudos for a correct solution.


I think it is E... Because there is no statement about how many tickets. "four different types of tickets"

1) He spent twice as much on C type than on G type... but maybe he bought 50 C types and 3 G types (??)<- the ratio can be anything
2) He spent at least 20 on each type of ticket: the problem I encounter from above still persists.


I think my reasoning here is probably wrong. Because it is lazy and if I just assume there is total 4 tickets I could probably put up an equation. I wish there was no room for interpretation, ever, on the GMAT! I'm a native speaker but often I fail to understand the wording.
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Re: Albert spent $100 in total on four different types of scratch tickets, [#permalink]
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Total amount spent = $100
Let the four different types of scratch tickets be B-type, C-type, G-type and M-type

B \(\leq$40\), C \(\leq$40\), G \(\leq$40\), and M \(\leq$40\)

Statement (1):
Albert spent twice as much on C-type tickets as he did on G-type tickets.
C = 2G

Total = B + C + G + M
\($100\) = B + 2G + G + M
\($100\) = B + 3G + M; many possibilities
Not Sufficient

Statement (2):
Albert spent at least $20 on each type of ticket.
\($20\leq\) B, C, G, M \(\leq$40\); many possibilities
Not Sufficient

From (1) and (2)
Minimum amount = \($20\); Maximum amount = \($40\)
C = 2G; C = \($40\), G = \($20\)
\($100\) = B + 3G + M
B + M = \($100\) - \($60\)
B + M = \($40\)
Since the minimum amount is \($20\), then B = M = \($20\)
B = M = G = \($20\), C = \($40\); minimum amount spent \($20\)
Sufficient

Answer C
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Re: Albert spent $100 in total on four different types of scratch tickets, [#permalink]
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Bunuel wrote:
Albert spent $100 in total on four different types of scratch tickets, and he did not spend more than $40 on any one type of scratch ticket. How much did he spend on the scratch ticket on which he spent the least?

(1) Albert spent twice as much on C-type tickets as he did on G-type tickets.
(2) Albert spent at least $20 on each type of ticket.


Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION:

Solution: C

Statement (1) doesn’t tell us about the third or fourth type of ticket; INSUFFICIENT. Statement (2) gives a range but no specific values; INSUFFICIENT. Taken together, you can set up the equation that 2G = C (if you double the amount he spent on G-types that equals the amount he spent on C-types), and that then 2G + G + x + y = 100. Since we know that x and y each have to be, at a minimum, $20, that limit helps you get to one exact combination. 3G + 20 + 20 = 100 means that 3G = 60, and that G = 20 and C = 40. And since that's the only way to combine all the terms to get to $100 with a minimum value of $20, you know that he spent $20 on the item on which he spent the least. The answer, thus, is (C).
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Re: Albert spent $100 in total on four different types of scratch tickets, [#permalink]
Honestly, I done understand why B is not the answer..

If he spends at least $20 on the ticket then $20 is the least possible amount that he spent on the ticket??

Explanations would be welcomed..
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Re: Albert spent $100 in total on four different types of scratch tickets, [#permalink]
Expert Reply
Tmoni26 wrote:
Honestly, I done understand why B is not the answer..

If he spends at least $20 on the ticket then $20 is the least possible amount that he spent on the ticket??

Explanations would be welcomed..


When a DS question asks about the value of some variable, then the statement(s) is sufficient ONLY if you can get the single numerical value of this variable.

From (2) it's possible that the prices are 20, 25, 25, 30 OR 25, 25, 25, 25, OR 21, 22, 23, 34, ...
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Re: Albert spent $100 in total on four different types of scratch tickets, [#permalink]
Expert Reply
Bunuel wrote:
Albert spent $100 in total on four different types of scratch tickets, and he did not spend more than $40 on any one type of scratch ticket. How much did he spend on the scratch ticket on which he spent the least?

(1) Albert spent twice as much on C-type tickets as he did on G-type tickets.
(2) Albert spent at least $20 on each type of ticket.

\(B,C,D,G\,\, \ge 0\,\,\,(\$ \,\,{\rm{spent}}\,\,{\rm{in}}\,\,{\rm{each}}\,\,{\rm{type}})\)

\(B + C + D + G = 100\)

\(B,C,D,G\,\,\, \le \,\,40\)


\(? = \min \left\{ {B,C,D,G} \right\}\)


\(\left( 1 \right)\,C = 2G\,\,\,\left\{ \matrix{\\
\,{\rm{Take}}\,\,\left( {B,C,D,G} \right) = \left( {10,40,30,20} \right)\,\,\, \Rightarrow \,\,\,? = 10 \hfill \cr \\
\,{\rm{Take}}\,\,\left( {B,C,D,G} \right) = \left( {5,40,35,20} \right)\,\,\, \Rightarrow \,\,\,? = 5 \hfill \cr} \right.\)


\(\left( 2 \right)\,\,B,C,D,G\,\,\, \ge \,\,20\,\,\,\left\{ \matrix{\\
\,{\rm{Take}}\,\,\left( {B,C,D,G} \right) = \left( {20,25,25,30} \right)\,\,\, \Rightarrow \,\,\,? = 20 \hfill \cr \\
\,{\rm{Take}}\,\,\left( {B,C,D,G} \right) = \left( {21,22,23,34} \right)\,\,\, \Rightarrow \,\,\,? = 21 \hfill \cr} \right.\)


\(\left( {1 + 2} \right)\,\,\left\{ \matrix{\\
G \ge 20\,\,\, \Rightarrow \,\,\,C \ge 40 \hfill \cr \\
B \ge 20 \hfill \cr} \right.\,\,\,\, \Rightarrow \,\,\,D \le 100 - \left( {20 + 20 + 40} \right) = 20\)


\({\rm{Hence}}:\,\,\left( {B,C,D,G} \right) = \left( {20,40,20,20} \right)\,\,\,\,\,\, \Rightarrow \,\,\,? = 20\)


The correct answer is therefore (C).


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: Albert spent $100 in total on four different types of scratch tickets, [#permalink]
Bunuel wrote:
Albert spent $100 in total on four different types of scratch tickets, and he did not spend more than $40 on any one type of scratch ticket. How much did he spend on the scratch ticket on which he spent the least?

(1) Albert spent twice as much on C-type tickets as he did on G-type tickets.
(2) Albert spent at least $20 on each type of ticket.


Kudos for a correct solution.


I think i read too much into the question.

It says we spend 100$ on 4-types of tickets. Does not say that we only bought total 4 tickets. We can have multiple tickets for a particular type.
Both the factual statements mention the types while the final question mentions on a particular ticket.

How do i make sure the inference is correct?
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Re: Albert spent $100 in total on four different types of scratch tickets, [#permalink]
Expert Reply
Bunuel wrote:
Albert spent $100 in total on four different types of scratch tickets, and he did not spend more than $40 on any one type of scratch ticket. How much did he spend on the scratch ticket on which he spent the least?

(1) Albert spent twice as much on C-type tickets as he did on G-type tickets.
(2) Albert spent at least $20 on each type of ticket.


We need to determine the least amount Albert spent on one type of scratch tickets, given that he spent a total of $100 on 4 different types of tickets, and he spent no more than $40 on any one type of ticket.

Statement One Alone:

Albert spent twice as much on C-type tickets as he did on G-type tickets.

If he spent $40 on the C-type tickets, then he spent $20 on the G-type tickets. He could have spent $20 and $20 on the other two types of tickets OR $30 and $10 on the other two types of tickets. In the former scenario, the least he spent on any type of ticket is $20. In the latter scenario, the least he spent is $10. Statement one alone is not sufficient.

Statement Two Alone:

Albert spent at least $20 on each type of ticket.

If he spent at least $20 on each type of ticket and we are given that he spent at most $40 on any one type of ticket. It is possible that he spent $40, $20, $20 and $20 on the 4 types of tickets OR $25 on each of the 4 types of tickets. In the former scenario, the least he spent on any type of ticket is $20. In the latter scenario, the least he spent is $25. Statement two alone is not sufficient.

Statements One and Two Together:

With the two statements together we see that he must have spent $40 on the C-type tickets, $20 on the G-type tickets and also $20 on each of the other 2 types of tickets. Therefore, the least he spent on any type of ticket is $20.

Answer: C
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Re: Albert spent $100 in total on four different types of scratch tickets, [#permalink]
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Re: Albert spent $100 in total on four different types of scratch tickets, [#permalink]
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