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# At the beginning of the day, a store had grills and smokers in a ratio

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At the beginning of the day, a store had grills and smokers in a ratio  [#permalink]

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14 Mar 2018, 21:22
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At the beginning of the day, a store had grills and smokers in a ratio of 3 to 4. If no new items were added to the store and the only items that left were those that were sold, what was the ratio of grills to smokers at the end of the day?

(1) There were 12 grills and 16 smokers sold

(2) One third of the grills were sold

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Re: At the beginning of the day, a store had grills and smokers in a ratio  [#permalink]

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14 Mar 2018, 21:52
G:S=3:4=3X:4X
1. g:s=3X-12:4X-16 ------------->NS
2. g:s=3X-X:4X =2X:4X =1:2 ------------->S

Thus I would like to go for B
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Re: At the beginning of the day, a store had grills and smokers in a ratio  [#permalink]

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14 Mar 2018, 22:28
1
1
Bunuel wrote:
At the beginning of the day, a store had grills and smokers in a ratio of 3 to 4. If no new items were added to the store and the only items that left were those that were sold, what was the ratio of grills to smokers at the end of the day?

(1) There were 12 grills and 16 smokers sold

(2) One third of the grills were sold

Let initial number of grills = 3x and initial number of smokers = 4x.

Statement 1:
new ratio of grills : smokers = (3x-12) : (4x-16)
Whats interesting here is that the grills and smokers sold are also in the ratio 3:4 only (12:16 = 3:4). Since initially they were in the ratio 3:4 and they are sold in the ratio 3:4 so the new ratio will also be 3:4.

Algebraically, we can see this way = (3x-12)/(4x-16)
Taking 3 common from numerator and 4 common from denominator we have = 3*(x-4) / 4*(x-4)
x-4 cancels from both numerator/denominator leaving 3/4 only, or the new ratio also is 3:4. Sufficient.

Statement 2:
1/3 grills sold, so grills left = 2/3 * 3x = 2x. But there is no information about number of smokers sold. So not sufficient.

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Re: At the beginning of the day, a store had grills and smokers in a ratio  [#permalink]

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14 Mar 2018, 22:35
amanvermagmat wrote:
Bunuel wrote:
At the beginning of the day, a store had grills and smokers in a ratio of 3 to 4. If no new items were added to the store and the only items that left were those that were sold, what was the ratio of grills to smokers at the end of the day?

(1) There were 12 grills and 16 smokers sold

(2) One third of the grills were sold

Let initial number of grills = 3x and initial number of smokers = 4x.

Statement 1:
new ratio of grills : smokers = (3x-12) : (4x-16)
Whats interesting here is that the grills and smokers sold are also in the ratio 3:4 only (12:16 = 3:4). Since initially they were in the ratio 3:4 and they are sold in the ratio 3:4 so the new ratio will also be 3:4.

Algebraically, we can see this way = (3x-12)/(4x-16)
Taking 3 common from numerator and 4 common from denominator we have = 3*(x-4) / 4*(x-4)
x-4 cancels from both numerator/denominator leaving 3/4 only, or the new ratio also is 3:4. Sufficient.

Statement 2:
1/3 grills sold, so grills left = 2/3 * 3x = 2x. But there is no information about number of smokers sold. So not sufficient.

I completely get my mistake of overlooking 12:16=3:4 for statement
But for statement 2, why we have to assume that there must be some numbers of Smokers sold.
Can't we assume 'nothing mentioned =0 sold' ?
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Re: At the beginning of the day, a store had grills and smokers in a ratio  [#permalink]

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14 Mar 2018, 22:43
u1983 wrote:
amanvermagmat wrote:
Bunuel wrote:
At the beginning of the day, a store had grills and smokers in a ratio of 3 to 4. If no new items were added to the store and the only items that left were those that were sold, what was the ratio of grills to smokers at the end of the day?

(1) There were 12 grills and 16 smokers sold

(2) One third of the grills were sold

Let initial number of grills = 3x and initial number of smokers = 4x.

Statement 1:
new ratio of grills : smokers = (3x-12) : (4x-16)
Whats interesting here is that the grills and smokers sold are also in the ratio 3:4 only (12:16 = 3:4). Since initially they were in the ratio 3:4 and they are sold in the ratio 3:4 so the new ratio will also be 3:4.

Algebraically, we can see this way = (3x-12)/(4x-16)
Taking 3 common from numerator and 4 common from denominator we have = 3*(x-4) / 4*(x-4)
x-4 cancels from both numerator/denominator leaving 3/4 only, or the new ratio also is 3:4. Sufficient.

Statement 2:
1/3 grills sold, so grills left = 2/3 * 3x = 2x. But there is no information about number of smokers sold. So not sufficient.

I completely get my mistake of overlooking 12:16=3:4 for statement
But for statement 2, why we have to assume that there must be some numbers of Smokers sold.
Can't we assume 'nothing mentioned =0 sold' ?

Hello

I think we cannot assume that. When nothing is mentioned about smokers, then their sales could be anything from 0 and upwards.
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At the beginning of the day, a store had grills and smokers in a ratio  [#permalink]

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Updated on: 20 Mar 2018, 12:15
1
At the Beginning:
Let CM for ratio be x
Grills: 3x
Smokers: 4x

St.1:
Sold- Grills:12, Smokers:16
Left behind- Grills: 3x-12, Smokers: 4x-16
Ratio at the end of the day:
G/S= (3x-12)/(4x-16)= 3(x-4)/4(x-4)= 3/4

Sufficient.

St.2: Grills sold= 3x/3= x
Grills left= 2x. No information on numbers of smokers sold. Insufficient.

Ans A

Originally posted by Shobhit7 on 16 Mar 2018, 04:21.
Last edited by Shobhit7 on 20 Mar 2018, 12:15, edited 2 times in total.
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Re: At the beginning of the day, a store had grills and smokers in a ratio  [#permalink]

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20 Mar 2018, 02:54
St1 3x-12/4x-16=3/4

Hence A
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Re: At the beginning of the day, a store had grills and smokers in a ratio  [#permalink]

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23 Mar 2018, 23:12
amanvermagmat wrote:
Bunuel wrote:
At the beginning of the day, a store had grills and smokers in a ratio of 3 to 4. If no new items were added to the store and the only items that left were those that were sold, what was the ratio of grills to smokers at the end of the day?

(1) There were 12 grills and 16 smokers sold

(2) One third of the grills were sold

Let initial number of grills = 3x and initial number of smokers = 4x.

Statement 1:
new ratio of grills : smokers = (3x-12) : (4x-16)
Whats interesting here is that the grills and smokers sold are also in the ratio 3:4 only (12:16 = 3:4). Since initially they were in the ratio 3:4 and they are sold in the ratio 3:4 so the new ratio will also be 3:4.

Algebraically, we can see this way = (3x-12)/(4x-16)
Taking 3 common from numerator and 4 common from denominator we have = 3*(x-4) / 4*(x-4)
x-4 cancels from both numerator/denominator leaving 3/4 only, or the new ratio also is 3:4. Sufficient.

Statement 2:
1/3 grills sold, so grills left = 2/3 * 3x = 2x. But there is no information about number of smokers sold. So not sufficient.

i made a big mistake thinking that initial inventory would have been 12 and 16 , so post the sale the items left would be zero. but the question stem says, there were items left in the store.
is that the reason we, didnt consider 12 and 16 as initial values.
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24 Mar 2018, 06:14
Yeah, but what if there are 12 grills and 16 smokers in the first place?
Then answer A is NOT SUFFICIENT, because, if we sell everything, the ratio is 0:0, or 1:1, certainly not 3:4.
Then the right answer is C, because we now know that in total there were more than 12 grills and 16 smokers.

And yes, 3*(x-4)/4*(x-4) = 3/4, but not if x=4, because we cannot divide by 0

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Re: At the beginning of the day, a store had grills and smokers in a ratio  [#permalink]

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24 Mar 2018, 10:56
urbanoc wrote:
Yeah, but what if there are 12 grills and 16 smokers in the first place?
Then answer A is NOT SUFFICIENT, because, if we sell everything, the ratio is 0:0, or 1:1, certainly not 3:4.
Then the right answer is C, because we now know that in total there were more than 12 grills and 16 smokers.

And yes, 3*(x-4)/4*(x-4) = 3/4, but not if x=4, because we cannot divide by 0

Experts?

Hello

the question stem says, "..only items that were left were those that were sold..". So some grills/smokers were left.

And 0:0 doesnt make any sense at all. We cannot take ratios of something that doesnt exist, so I believe we can safely discard that possibility here (or 0 smokers or 0 grills left at the end of day).
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Re: At the beginning of the day, a store had grills and smokers in a ratio  [#permalink]

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25 Mar 2018, 08:22
amanvermagmat wrote:
urbanoc wrote:
Yeah, but what if there are 12 grills and 16 smokers in the first place?
Then answer A is NOT SUFFICIENT, because, if we sell everything, the ratio is 0:0, or 1:1, certainly not 3:4.
Then the right answer is C, because we now know that in total there were more than 12 grills and 16 smokers.

And yes, 3*(x-4)/4*(x-4) = 3/4, but not if x=4, because we cannot divide by 0

Experts?

Hello

the question stem says, "..only items that were left were those that were sold..". So some grills/smokers were left.

And 0:0 doesnt make any sense at all. We cannot take ratios of something that doesnt exist, so I believe we can safely discard that possibility here (or 0 smokers or 0 grills left at the end of day).

Hi amanvermagmat, thanks for the reply!

The question stem doesn't say like you wrote " the only items that WERE left, were those that were sold",

the question states: "the only items that left were those that were sold", so it is possible to sell everything, so it possible to have at the end 0 (zero) items in the inventory.
I still don't understand why we should assume that not everything can be sold.
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Re: At the beginning of the day, a store had grills and smokers in a ratio  [#permalink]

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25 Mar 2018, 21:54
urbanoc wrote:
amanvermagmat wrote:
urbanoc wrote:
Yeah, but what if there are 12 grills and 16 smokers in the first place?
Then answer A is NOT SUFFICIENT, because, if we sell everything, the ratio is 0:0, or 1:1, certainly not 3:4.
Then the right answer is C, because we now know that in total there were more than 12 grills and 16 smokers.

And yes, 3*(x-4)/4*(x-4) = 3/4, but not if x=4, because we cannot divide by 0

Experts?

Hello

the question stem says, "..only items that were left were those that were sold..". So some grills/smokers were left.

And 0:0 doesnt make any sense at all. We cannot take ratios of something that doesnt exist, so I believe we can safely discard that possibility here (or 0 smokers or 0 grills left at the end of day).

Hi amanvermagmat, thanks for the reply!

The question stem doesn't say like you wrote " the only items that WERE left, were those that were sold",

the question states: "the only items that left were those that were sold", so it is possible to sell everything, so it possible to have at the end 0 (zero) items in the inventory.
I still don't understand why we should assume that not everything can be sold.

Hello

The only explanation I have to your query is that if everything gets sold, then the number of smokers remaining = number of grills remaining = 0, thus the ratio 0:0 doesnt make any sense. I think such a thing will not be tested in a question, where there is a possibility that we have to take ratio of non-existent quantities.
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Re: At the beginning of the day, a store had grills and smokers in a ratio  [#permalink]

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26 Mar 2018, 02:24
Hello

the question stem says, "..only items that were left were those that were sold..". So some grills/smokers were left.

And 0:0 doesnt make any sense at all. We cannot take ratios of something that doesnt exist, so I believe we can safely discard that possibility here (or 0 smokers or 0 grills left at the end of day).[/quote]

Hi amanvermagmat, thanks for the reply!

The question stem doesn't say like you wrote " the only items that WERE left, were those that were sold",

the question states: "the only items that left were those that were sold", so it is possible to sell everything, so it possible to have at the end 0 (zero) items in the inventory.
I still don't understand why we should assume that not everything can be sold.[/quote]

Hello

The only explanation I have to your query is that if everything gets sold, then the number of smokers remaining = number of grills remaining = 0, thus the ratio 0:0 doesnt make any sense. I think such a thing will not be tested in a question, where there is a possibility that we have to take ratio of non-existent quantities.[/quote]

Hi,

I know what you mean, and if we were in a Problem Solving question I would think the same. But since we are in a DS question, one should analyse all possibilities...
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At the beginning of the day, a store had grills and smokers in a ratio  [#permalink]

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26 Mar 2018, 09:32
Guys!

I have a doubt about the OA. The First statement is correct for all situations except for one. ie. if at the beginning of the day, there were only 12 & 16 , grills & cookers respectively. At the end of the day, in such a scenario, there will be 0 of both. Hence, negating the OA.

Bunuel Please let me know, if there is any flaw in the situation i have mentioned above. I solved it using that logic & chose C as it takes care of the issue.
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29 Mar 2018, 12:24
I think selling 12 and 16 is a totally valid situation. Nothing stops it and the fact that it creates a non-sensical 0:0, if anything, sounds like proof that the answer isn't A.

Since (2) helps to guarantee that the inventory isn't going to be totally sold out, the answer should be (C) imo.
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25 Dec 2018, 06:32
From such a topic about grill, I honestly wanted to eat. so I’ll probably go get my grill go to this website and make something delicious for our family for dinner.
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At the beginning of the day, a store had grills and smokers in a ratio  [#permalink]

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10 Apr 2019, 13:37
For (I), what if, the store had only 12 grills and 16 smokers. This leads to 0:0 , hence, insufficient.
For (II), I understand why it is insufficient.

When they are taken together, C is correct. Why am I wrong in selecting (C) as the answer?
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Re: At the beginning of the day, a store had grills and smokers in a ratio  [#permalink]

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11 Apr 2019, 07:07
I'm confused : the only items that left were those that were sold ?
shouldn't it be the only items that left were those that were NOT sold ?
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Re: At the beginning of the day, a store had grills and smokers in a ratio  [#permalink]

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23 May 2019, 22:39
Top Contributor
Really good discussion here! And I agree that the possibility of starting with 12 and 16 and selling all of them to get to a final tally of 0 and 0 makes this one problematic. As you can see from the discussion it's controversial enough among really thoughtful people that I doubt GMAC would ever ask it in its current form. I *do* know that the rule we're gong for here is very testable (if you add/subtract in the same ratio as the original, you can infer that the ratio doesn't change), but for this to be a valid problem it does likely require ruling out the "everything got sold, so there's nothing left" possibility. I've updated the question in our database to the following:

At the beginning of the day, a store had grills and smokers in a ratio of 3 to 4. No new items were added to the store and the only items that left the store were those that were sold. If not all grills and smokers were sold during the day, what was the ratio of grills to smokers at the end of the day?

(1) There were 12 grills and 16 smokers sold

(2) One third of the grills were sold

Note, too, that GMAC has a few unscored, experimental questions per section that are there to just get data to tell things like how difficult they are *and* whether there's ambiguity like you see here. The questions that count have all been thoroughly vetted by testing, and we do the same thing via our Question Bank so discussions like this are really valuable. Thank you, everyone!
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Re: At the beginning of the day, a store had grills and smokers in a ratio   [#permalink] 23 May 2019, 22:39
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