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There are x highlevel officials (where x is a positive integer). Each
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03 Nov 2014, 09:15
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Tough and Tricky questions: Word Problems. There are x highlevel officials (where x is a positive integer). Each highlevel official supervises x^2 midlevel officials, each of whom, in turn, supervises x^3 lowlevel officials. How many highlevel officials are there? (1) There are fewer than 60 lowlevel officials. (2) No official is supervised by more than one person. Kudos for a correct solution.
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Re: There are x highlevel officials (where x is a positive integer). Each
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04 Nov 2014, 10:49
Statement 1 is clearly Insufficient as 1^3, 2^3, 3^3 all are less then 60.
Statement 2 tells that no official is supervised bt more than one person. x=1. Sufficient. Answer is B.



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Re: There are x highlevel officials (where x is a positive integer). Each
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04 Nov 2014, 21:38
Clearly, neither of statement 1 and 2 is sufficient.
Combining 1 and 2 :
From statement 1, the different combinations are : High officials = 1 , Mid level official = 1 , Low Level officials = 1 High officials = 2 , Mid level official = 4 , Low Level officials = 8 High officials = 3 , Mid level official = 9 , Low Level officials = 27
From statement 2, "No official is supervised by more than one person." , we cannot conclusively say which group we can pick.
Hence the answer is E



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Re: There are x highlevel officials (where x is a positive integer). Each
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04 Nov 2014, 23:05
There are x highlevel officials (where x is a positive integer). Each highlevel official supervises x^2 midlevel officials, each of whom, in turn, supervises x^3 lowlevel officials. How many highlevel officials are there? (1) There are fewer than 60 lowlevel officials. (2) No official is supervised by more than one person. xx^2(each of whom)x^3 1) 248 (8*4= 32) 32<60 yes 3927 (27*9= 243) 243<60 no thus 4 high level officials 2) insufficient thus A. OA please.
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Re: There are x highlevel officials (where x is a positive integer). Each
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06 Nov 2014, 14:57
Not sure if i'm on the wrong track here but 1 looks sufficient to me.
2 high (test): 2, each of which supervises 2^2 (so 4). So 2 * 4 = 8 mids.
8 mids
low level? 8, each of which supervises 2^3 (=8), so 8*8 = 64. Too large for statement 1 to hold, therefore 1 high official  sufficient.
statement 2 makes no sense to me so I think its a distractor, therefore A.



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Re: There are x highlevel officials (where x is a positive integer). Each
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07 Nov 2014, 00:57
Bunuel When will the OA be updated for these questions??



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Re: There are x highlevel officials (where x is a positive integer). Each
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07 Nov 2014, 04:24
sunaimshadmani wrote: Bunuel When will the OA be updated for these questions?? The OA's will be announced on this weekend.
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Re: There are x highlevel officials (where x is a positive integer). Each
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07 Nov 2014, 22:53
The key is EACH OF which means if there are 2 high level there are 8 mid level and 8*8=64 low level. So A looks sufficient BUT, the stem does not say the low level cannot report to more than one mid level managers. Say that 5 low level report to 2 mid level managers, then there can be 1 or 2 high level managers  so not sufficient. B resolves this if no one has more than one manager the only solution is to have 1 high level, 1 mid level and 1 low level. C combined sufficient. Posted from GMAT ToolKit



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Re: There are x highlevel officials (where x is a positive integer). Each
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08 Nov 2014, 14:32
If x = 1, then there's 1 high level, 1 med level, and 1 low level If x = 2, there's 2 high level, each of whom supervise x^2 = 4, for a total of 8 mid level, each of whom supervise x^3 = 8 for 64 low level.
1 alone: tells you fewer than 60 low level, but x could equal 2 if low level employees report to more than one manager. 2 alone: could be any value for x
1 & 2 combined allow you to definitively answer, so answer is C



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Re: There are x highlevel officials (where x is a positive integer). Each
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10 Nov 2014, 03:46
Let H,M and L represent High,Medium and Low level officers resp. By given condition: if H=1 then M=1 and L=1 if H=2 then M=2*(2^2)=8 and L=8*(2^3)=64
(1) It tells us that L<60, thus only first of the above two situations satisfies. i.e H=1, it won't be true if H>1>Sufficient (2) In each of the above two situations, No official is supervised by more than one person as it is given in the question statement itself that each of relatively higher level officers supervise a set of lower level officers> insufficient
Hence, the correct answer is choice(A)



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Re: There are x highlevel officials (where x is a positive integer). Each
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23 Apr 2015, 00:43
Bunuel wrote: Tough and Tricky questions: Word Problems. There are x highlevel officials (where x is a positive integer). Each highlevel official supervises x^2 midlevel officials, each of whom, in turn, supervises x^3 lowlevel officials. How many highlevel officials are there? (1) There are fewer than 60 lowlevel officials. (2) No official is supervised by more than one person. Kudos for a correct solution.Hi Bunuel, I marked A. Could you please explain how does B contribute to the solution. Thanks in advance. aimtoteach
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Re: There are x highlevel officials (where x is a positive integer). Each
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23 Apr 2015, 01:27
Bunuel wrote: Tough and Tricky questions: Word Problems. There are x highlevel officials (where x is a positive integer). Each highlevel official supervises x^2 midlevel officials, each of whom, in turn, supervises x^3 lowlevel officials. How many highlevel officials are there? (1) There are fewer than 60 lowlevel officials. (2) No official is supervised by more than one person. Kudos for a correct solution.I also marked A, not sure how statement 1 contributes to the answer... My reasoning: Statement 1: tells us that x^3<60 Statement 2: no official is supervised by more than one person: insinuates that x = x^2 = x^3 ... I thought this could only be true for x=1 Please clear up



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Re: There are x highlevel officials (where x is a positive integer). Each
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23 Apr 2015, 01:34
sabineodf wrote: Bunuel wrote: Tough and Tricky questions: Word Problems. There are x highlevel officials (where x is a positive integer). Each highlevel official supervises x^2 midlevel officials, each of whom, in turn, supervises x^3 lowlevel officials. How many highlevel officials are there? (1) There are fewer than 60 lowlevel officials. (2) No official is supervised by more than one person. Kudos for a correct solution.I also marked A, not sure how statement 1 contributes to the answer... My reasoning: Statement 1: tells us that x^3<60 Statement 2: no official is supervised by more than one person: insinuates that x = x^2 = x^3 ... I thought this could only be true for x=1 Please clear up Reread my reasoning and the question and I retract my statements haha but I am still confused about the questions. I still don't understand how to get the answer though! But I've realized that statement 1 has more value than I initially thought because it has narrowed the options of x down to 1, 2 or 3... So what is B giving us that tells us which one it is?



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Re: There are x highlevel officials (where x is a positive integer). Each
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23 Apr 2015, 03:11
aimtoteach wrote: Bunuel wrote: Tough and Tricky questions: Word Problems. There are x highlevel officials (where x is a positive integer). Each highlevel official supervises x^2 midlevel officials, each of whom, in turn, supervises x^3 lowlevel officials. How many highlevel officials are there? (1) There are fewer than 60 lowlevel officials. (2) No official is supervised by more than one person. Kudos for a correct solution.Hi Bunuel, I marked A. Could you please explain how does B contribute to the solution. Thanks in advance. aimtoteach Hello aimtoteach and sabineodfLet's imagine that we have firm with 10 low level workers and 2 managers. But we know nothing about hierarchy of this firm. Maybe each manager has 5 dedicated subordinates or maybe it's mix hierarchy and each manager has 10 subordinates: each from this employees has two managers and report to each managers for different tasks. Second statement clarify situation about hierarchy of firm from the task.
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There are x highlevel officials (where x is a positive integer). Each
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08 Mar 2016, 10:41
There are x highlevel officials (where x is a positive integer). Each highlevel official supervises x2 midlevel officials, each of whom, in turn, supervises x3 lowlevel officials. How many highlevel officials are there?
(1) There are fewer than 60 lowlevel officials.
(2) No official is supervised by more than one person.



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Re: There are x highlevel officials (where x is a positive integer). Each
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08 Mar 2016, 12:00
APARNASHAH wrote: There are x highlevel officials (where x is a positive integer). Each highlevel official supervises x2 midlevel officials, each of whom, in turn, supervises x3 lowlevel officials. How many highlevel officials are there?
(1) There are fewer than 60 lowlevel officials.
(2) No official is supervised by more than one person. Merging topics. Please search before posting.
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Re: There are x highlevel officials (where x is a positive integer). Each
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03 Oct 2016, 07:51
Hi Bunuel, could you please post explanation why is it not E?



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Re: There are x highlevel officials (where x is a positive integer). Each
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15 Jan 2017, 17:40
Let's assume that there are 2 high level officials. This means that each of these 2 high level officials supervises 4 (or x^2) midlevel officials, and that each of these 4 midlevel officials supervises 8 (or x^3) lowlevel officials. It is possible that the supervisors do not share any subordinates. If this is the case, then, given 2 high level officials, there must be 2(4) = 8 midlevel officials, and 8(8) = 64 lowlevel officials. Alternatively, it is possible that the supervisors share all or some subordinates. In other words, given 2 high level officials, it is possible that there are as few as 4 midlevel officials (as each of the 2 highlevel officials supervise the same 4 midlevel officials) and as few as 8 lowlevel officials (as each of the 4 midlevel officials supervise the same 8 lowlevel officials). Statement (1) tells us that there are fewer than 60 lowlevel officials. This alone does not allow us to determine how many highlevel officials there are. For example, there might be 2 high level officials, who each supervise the same 4 midlevel officials, who, in turn, each supervise the same 8 lowlevel officials. Alternatively, there might be 3 highlevel officials, who each supervise the same 9 midlevel officials, who, in turn, each supervise the same 27 lowlevel officials. Statement (2) tells us that no official is supervised by more than one person, which means that supervisors do not share any subordinates. Alone, this does not tell us anything about the number of highlevel officials. Combining statements 1 and 2, we can test out different possibilities. If x = 1, there is 1 highlevel official, who supervises 1 midlevel official (12 = 1), who, in turn, supervises 1 lowlevel official (13 = 1). If x = 2, there are 2 highlevel officials, who each supervise a unique group of 4 midlevel officials, yielding 8 midlevel officials in total. Each of these 8 midlevel officials supervise a unique group of 8 lowlevel officials, yielding 64 lowlevel officials in total. However, this cannot be the case since we are told that there are fewer than 60 lowlevel officials. Therefore, based on both statements taken together, there must be only 1 highlevel official. The correct answer is C: BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
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Re: There are x highlevel officials (where x is a positive integer). Each
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