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Anthony can purchase bagels at $1.99 for a specialty bagel and $15.99

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Anthony can purchase bagels at $1.99 for a specialty bagel and $15.99  [#permalink]

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New post 15 Feb 2017, 22:17
2
2
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A
B
C
D
E

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  45% (medium)

Question Stats:

69% (02:26) correct 31% (01:42) wrong based on 66 sessions

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Anthony can purchase bagels at \($1.99\) for a specialty bagel and \($15.99\) for a package of one dozen plain bagels. If Anthony can purchase only specialty bagels or packages of plain bagels, did Anthony purchase any plain bagels?

(1) Anthony spent less than \($32.00\)
(2) Anthony spent more than \($31.90\)

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Anthony can purchase bagels at $1.99 for a specialty bagel and $15.99  [#permalink]

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New post 15 Feb 2017, 23:47
ziyuenlau wrote:
Anthony can purchase bagels at \($1.99\) for a specialty bagel and \($15.99\) for a package of one dozen plain bagels. If Anthony can purchase only specialty bagels or packages of plain bagels, did Anthony purchase any plain bagels?

(1) Anthony spent less than \($32.00\)
(2) Anthony spent more than \($31.90\)

Dear ziyuenlau

I'm happy to respond. :-)

Normally, I like Veritas questions, but this is one I don't like. I find the beginning of the second sentence ambiguous-- "Anthony can purchase only specialty bagels or packages of plain bagels." I took this to be simply a clarification of the previous sentence: the only items for sale at this shop are individual specialty bagel and packages of 12 plain bagels, so his purchase can only include those two items. I was interpreting the word "or" as an inclusive "or," because the word "or" is always inclusive in mathematics. This interpretation leads to the answer (E), because with combined statements, the purchase could be either two dozen plain or one dozen plain + 8 specialty bagels.

The only way we can arrive at the answer (C) is if we interpret the "or" as an exclusive "or," in violation of the precedent throughout all mathematics. I suspect this question was written by an American thinking of the conventions of colloquial spoken English, rather than the conventions of mathematics.

I find this question problematic for these reasons. Let me know if anyone has any questions.

Mike :-)

NOTE: See my retraction of this position below. -- Mike
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Anthony can purchase bagels at $1.99 for a specialty bagel and $15.99  [#permalink]

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New post 16 Feb 2017, 00:28
mikemcgarry wrote:
ziyuenlau wrote:
Anthony can purchase bagels at \($1.99\) for a specialty bagel and \($15.99\) for a package of one dozen plain bagels. If Anthony can purchase only specialty bagels or packages of plain bagels, did Anthony purchase any plain bagels?

(1) Anthony spent less than \($32.00\)
(2) Anthony spent more than \($31.90\)

Dear ziyuenlau

I'm happy to respond. :-)

Normally, I like Veritas questions, but this is one I don't like. I find the beginning of the second sentence ambiguous-- "Anthony can purchase only specialty bagels or packages of plain bagels." I took this to be simply a clarification of the previous sentence: the only items for sale at this shop are individual specialty bagel and packages of 12 plain bagels, so his purchase can only include those two items. I was interpreting the word "or" as an inclusive "or," because the word "or" is always inclusive in mathematics. This interpretation leads to the answer (E), because with combined statements, the purchase could be either two dozen plain or one dozen plain + 8 specialty bagels.

The only way we can arrive at the answer (C) is if we interpret the "or" as an exclusive "or," in violation of the precedent throughout all mathematics. I suspect this question was written by an American thinking of the conventions of colloquial spoken English, rather than the conventions of mathematics.

I find this question problematic for these reasons. Let me know if anyone has any questions.

Mike :-)



Thanks Mike for your clarification. Although I'm non native speaker, I reached you conclusion above.

Sometimes Veritas through strange questions. May you provide your view on the following also? I posted my view but your view is appreciated.

https://gmatclub.com/forum/a-certain-fr ... l#p1806094


Thanks in advance
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Anthony can purchase bagels at $1.99 for a specialty bagel and $15.99  [#permalink]

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New post 16 Feb 2017, 01:42
2
mikemcgarry wrote:
ziyuenlau wrote:
Anthony can purchase bagels at \($1.99\) for a specialty bagel and \($15.99\) for a package of one dozen plain bagels. If Anthony can purchase only specialty bagels or packages of plain bagels, did Anthony purchase any plain bagels?

(1) Anthony spent less than \($32.00\)
(2) Anthony spent more than \($31.90\)

Dear ziyuenlau

I'm happy to respond. :-)

Normally, I like Veritas questions, but this is one I don't like. I find the beginning of the second sentence ambiguous-- "Anthony can purchase only specialty bagels or packages of plain bagels." I took this to be simply a clarification of the previous sentence: the only items for sale at this shop are individual specialty bagel and packages of 12 plain bagels, so his purchase can only include those two items. I was interpreting the word "or" as an inclusive "or," because the word "or" is always inclusive in mathematics. This interpretation leads to the answer (E), because with combined statements, the purchase could be either two dozen plain or one dozen plain + 8 specialty bagels.

The only way we can arrive at the answer (C) is if we interpret the "or" as an exclusive "or," in violation of the precedent throughout all mathematics. I suspect this question was written by an American thinking of the conventions of colloquial spoken English, rather than the conventions of mathematics.

I find this question problematic for these reasons. Let me know if anyone has any questions.

Mike :-)


I didn't write this question, but I was involved in its editing and I can verify that the "or" is intended as inclusive. Maybe we should have written "and/or"? You are correct, of course, that the inclusive "or" is standard on the GMAT. Why does this reading lead you to the answer E? Perhaps the question is not well worded in some other way? Note that the question is whether Anthony purchased *any* plain bagels.

P.s. I'm glad to hear that you normally like our questions. We try hard. :)

P.p.s. This question was written by an American who is conversant with both the conventions of colloquial spoken English and the conventions of mathematics (to the best of my knowledge).
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Re: Anthony can purchase bagels at $1.99 for a specialty bagel and $15.99  [#permalink]

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New post 16 Feb 2017, 11:29
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AnthonyRitz wrote:
I didn't write this question, but I was involved in its editing and I can verify that the "or" is intended as inclusive. Maybe we should have written "and/or"? You are correct, of course, that the inclusive "or" is standard on the GMAT. Why does this reading lead you to the answer E? Perhaps the question is not well worded in some other way? Note that the question is whether Anthony purchased *any* plain bagels.

P.s. I'm glad to hear that you normally like our questions. We try hard. :)

P.p.s. This question was written by an American who is conversant with both the conventions of colloquial spoken English and the conventions of mathematics (to the best of my knowledge).

Dear AnthonyRitz,

Yes, my friend! Kudos to you! :-) You are correct and I was wrong! Yes, in my concern about the nature of the "or," I misread the end of the prompt. My mistake! :oops:

Absolutely, if the price is between $31.90 and $32.00, it could have been
1) 8 specialty bagels + one dozen plain = 8($2.00 - 1¢) + ($16 - 1¢) = $32.00 - 9¢ = $31.91
or
2) two dozen plain = 2($16 - 1¢) = $32.00 - 2¢ = $31.98
but as you astutely point out, either combination involves at least some plain. If we tried to fill the order with all specialty bagels, we would get,
3) 16 specialty bagels = 16($2.00 - 1¢) = $32.00 - 16¢ = $31.84
Thus, we absolutely need to have at least some plain bagels. This is a brilliantly constructed question, like so many of Veritas', and the answer is unambiguously (C).

Although the question is rigorously correct as is, it may prevent any future possible confusion by stating something such as this: "If the shop only sells these two options, and if Anthony can purchase any combination of individual specialty bagels and packages of plain bagels, then . . ." That's my suggestion: as we both know, the GMAT often over-specifies to ensure clarity and unambiguity.

Overall, Anthony, I apologize for my harsh judgment. Kudos to you and your colleagues at Veritas: you are an impressively bright bunch of folks!

With great respect,
Mike McGarry :-)
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Anthony can purchase bagels at $1.99 for a specialty bagel and $15.99  [#permalink]

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New post 16 Feb 2017, 11:33
Mike,

No worries! I appreciate what you do here! We're all going to mess up sooner or later among hundreds or thousands of GMAT questions.

Your wording suggestion makes sense, and I'm happy to pass it along to the question author and see about editing this.

EDIT: "At a certain bagel shop, Anthony can purchase bagels at $1.99 for one specialty bagel and $15.99 for a package of one dozen plain bagels. If the shop only sells these two options, and if Anthony can purchase any combination of individual specialty bagels and packages of plain bagels, then did Anthony purchase any plain bagels?"

I hope that's clearer!

mikemcgarry wrote:
AnthonyRitz wrote:
I didn't write this question, but I was involved in its editing and I can verify that the "or" is intended as inclusive. Maybe we should have written "and/or"? You are correct, of course, that the inclusive "or" is standard on the GMAT. Why does this reading lead you to the answer E? Perhaps the question is not well worded in some other way? Note that the question is whether Anthony purchased *any* plain bagels.

P.s. I'm glad to hear that you normally like our questions. We try hard. :)

P.p.s. This question was written by an American who is conversant with both the conventions of colloquial spoken English and the conventions of mathematics (to the best of my knowledge).

Dear AnthonyRitz,

Yes, my friend! Kudos to you! :-) You are correct and I was wrong! Yes, in my concern about the nature of the "or," I misread the end of the prompt. My mistake! :oops:

Absolutely, if the price is between $31.90 and $32.00, it could have been
1) 8 specialty bagels + one dozen plain = 8($2.00 - 1¢) + ($16 - 1¢) = $32.00 - 9¢ = $31.91
or
2) two dozen plain = 2($16 - 1¢) = $32.00 - 2¢ = $31.98
but as you astutely point out, either combination involves at least some plain. If we tried to fill the order with all specialty bagels, we would get,
3) 16 specialty bagels = 16($2.00 - 1¢) = $32.00 - 16¢ = $31.84
Thus, we absolutely need to have at least some plain bagels. This is a brilliantly constructed question, like so many of Veritas', and the answer is unambiguously (C).

Although the question is rigorously correct as is, it may prevent any future possible confusion by stating something such as this: "If the shop only sells these two options, and if Anthony can purchase any combination of individual specialty bagels and packages of plain bagels, then . . ." That's my suggestion: as we both know, the GMAT often over-specifies to ensure clarity and unambiguity.

Overall, Anthony, I apologize for my harsh judgment. Kudos to you and your colleagues at Veritas: you are an impressively bright bunch of folks!

With great respect,
Mike McGarry :-)
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Re: Anthony can purchase bagels at $1.99 for a specialty bagel and $15.99  [#permalink]

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New post 26 Dec 2017, 10:57
Hi All,

This question ultimately comes down to 'limited options' and whether they actually exist or not with the given information. In real basic terms, this question can be re-written as "Are there any '15.99s' in the group?" This is a YES/NO question.

1) Anthony spent less than $32.00

There could be one or two 15.99s in the group, in which case the answer would be YES
There might not be a 15.99 in the group, in which case the answer would be NO
Fact 1 is INSUFFICIENT

2) Anthony spent more than $31.90

There could be one or more 15.99s in the group, in which case the answer would be YES
There might not be a 15.99 in the group, in which case the answer would be NO
Fact 2 is INSUFFICIENT

Combined, we have a very narrow "window" ($31.90 < TOTAL < $32.00).

IF....there were two $15.99s, then the total would be $31.98 and the answer to the question would be YES
IF....there was one $15.99 and eight $1.99s, then the total would be $31.91 and the answer to the question would be YES
IF... there were NO $15.99s, then we would have just $1.99s; however - with 16 of them we have a total of $31.84 and with 17 of them we have a total of $33.83. Thus, there is NO WAY to get into the given range if we have zero $15.99s, so there isn't a NO answer under these circumstances. Thus, the answer to the question is ALWAYS YES.

Final Answer:

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Re: Anthony can purchase bagels at $1.99 for a specialty bagel and $15.99 &nbs [#permalink] 26 Dec 2017, 10:57
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