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Nine identical chips are numbered from 1 to 9 (one different number pe
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25 Feb 2019, 08:06
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Question Stats:
44% (02:00) correct 56% (02:28) wrong based on 34 sessions
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GMATH practice exercise (Quant Class 18)
Nine identical chips are numbered from 1 to 9 (one different number per chip) and placed in a box. There are N ways in which all the chips are taken out from the box, one at a time and without repositions, in a sequence of alternating odd and even numbers. The value of N is:
(A) less than 1400 (B) between 1400 and 2000 (C) between 2000 and 2600 (D) between 2600 and 3200 (E) greater than 3200
Re: Nine identical chips are numbered from 1 to 9 (one different number pe
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25 Feb 2019, 08:34
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fskilnik wrote:
GMATH practice exercise (Quant Class 18)
Nine identical chips are numbered from 1 to 9 (one different number per chip) and placed in a box. There are N ways in which all the chips are taken out from the box, one at a time and without repositions, in a sequence of alternating odd and even numbers. The value of N is:
(A) less than 1400 (B) between 1400 and 2000 (C) between 2000 and 2600 (D) between 2600 and 3200 (E) greater than 3200
ODDS: 1, 3, 5, 7, 9 EVENS: 2, 4, 6, 8
Take the task of removing the 9 chips and break it into stages.
Stage 1: Select an ODD number to be the 1st selection There are 5 ODDs to choose from. So, we can complete stage 1 in 5 ways
Stage 2: Select an EVEN number to be the 2nd selection There are 4 EVENs to choose from. So, we can complete stage 2 in 4 ways
Stage 3: Select an ODD number to be the 3rd selection There are 4 ODDs remaining. So, we can complete this stage in 4 ways
Stage 4: Select an EVEN number to be the 4th selection There are 3 EVENs remaining. So, we can complete this stage in 3 ways
Stage 5: Select an ODD number to be the 5th selection There are 3 ODDs remaining. So, we can complete this stage in 3 ways
Stage 6: Select an EVEN number to be the 6th selection There are 2 EVENs remaining. So, we can complete this stage in 2 ways
Stage 7: Select an ODD number to be the 7th selection There are 2 ODDs remaining. So, we can complete this stage in 2 ways
Stage 8: Select an EVEN number to be the 8th selection There is 1 EVEN number remaining. So, we can complete this stage in 1 way
Stage 9: Select an ODD number to be the 9th selection There is 1 ODD number remaining. So, we can complete this stage in 1 way
By the Fundamental Counting Principle (FCP), we can complete all 9 stages in (5)(4)(4)(3)(3)(2)(2)(1)(1) ways (= 2880 ways)
Answer: D
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.
Re: Nine identical chips are numbered from 1 to 9 (one different number pe
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25 Feb 2019, 13:52
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fskilnik wrote:
GMATH practice exercise (Quant Class 18)
Nine identical chips are numbered from 1 to 9 (one different number per chip) and placed in a box. There are N ways in which all the chips are taken out from the box, one at a time and without repositions, in a sequence of alternating odd and even numbers. The value of N is:
(A) less than 1400 (B) between 1400 and 2000 (C) between 2000 and 2600 (D) between 2600 and 3200 (E) greater than 3200
Re: Nine identical chips are numbered from 1 to 9 (one different number pe
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27 Feb 2019, 04:48
fskilnik wrote:
GMATH practice exercise (Quant Class 18)
Nine identical chips are numbered from 1 to 9 (one different number per chip) and placed in a box. There are N ways in which all the chips are taken out from the box, one at a time and without repositions, in a sequence of alternating odd and even numbers. The value of N is:
(A) less than 1400 (B) between 1400 and 2000 (C) between 2000 and 2600 (D) between 2600 and 3200 (E) greater than 3200
odd = 1,3,5,7,9 ; 5 digits and even = 2,4,6,8 so first odd then even can be taken out in sequence as; 5*4*4*3*3*2*2*1*1 = 2880 IMO D
gmatclubot
Re: Nine identical chips are numbered from 1 to 9 (one different number pe
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27 Feb 2019, 04:48