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29 Dec 2021, 09:15
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
53% (02:48) correct
47%
(03:04)
wrong
based on 59
sessions
History
Date
Time
Result
Not Attempted Yet
A traveller is stranded in an unknown town and needs to make a telephone call to her friend. Unfortunately, the traveller does not recall the seven digit telephone number. The traveller does recall that the first three digits of the number are either 635 or 674, that the number is odd, and that there is exactly one digit of '9' in the number. What is the minimum number of trials that the traveller needs to make to produce the correct telephone number?
(A) 3206
(B) 3402
(C) 5014
(D) 6018
(E) 8220
Are You Up For the Challenge: 700 Level Questions
(A) 3206
(B) 3402
(C) 5014
(D) 6018
(E) 8220
Are You Up For the Challenge: 700 Level Questions
Updated on: 29 Dec 2021, 22:08
Originally posted by gmatophobia on 29 Dec 2021, 13:22.
Last edited by gmatophobia on 29 Dec 2021, 22:08, edited 1 time in total.
Last edited by gmatophobia on 29 Dec 2021, 22:08, edited 1 time in total.
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Unlucky traveler ! Stranded on the island, she is unable to recollect the number of her friend. 
We know that the first three numbers are either 635 or 674, that the number is odd and that there is exactly one '9'.
6 3 5 _ _ _ _
As the number is odd, the last digit should end either in 1, 3, 5, 7, 9.
As there has to be exactly one 9 in the seven digit, we will handle that separately.
Case 1: Last digit is odd, but NOT 9.
6 3 5 _ _ _ 4
The last digit can therefore be filled in 4 ways using number 1, 3, 5, 7.
As there is exactly on 9 it can be in any of the middle three places.
The other two places can be filled in 9 ways (all digits from 0 to 9, except 9)
6 3 5 _ 9 9 4
Total Number of ways = 3 * 4 * 9 * 9 = 972 ways
Case 1: Last digit is 9.
So the last digit can be filled only in 1 way.
The remaining digits can be filled in 9 ways (all digits from 0 to 9, except 9)
6 3 5 9 9 9 1
Total Number of ways = 9 * 9 * 9 = 729 ways
Total number of ways = 729 + 972 = 1701 ways.
The same number of combinations would also apply for
6 7 54 _ _ _ _
Total number of possible combinations = 1701 * 2 = 3402.
IMO B
P.S - Looking at the number of possible combinations, it is likely that the person will be stranded for some more time
We know that the first three numbers are either 635 or 674, that the number is odd and that there is exactly one '9'.
6 3 5 _ _ _ _
As the number is odd, the last digit should end either in 1, 3, 5, 7, 9.
As there has to be exactly one 9 in the seven digit, we will handle that separately.
Case 1: Last digit is odd, but NOT 9.
6 3 5 _ _ _ 4
The last digit can therefore be filled in 4 ways using number 1, 3, 5, 7.
As there is exactly on 9 it can be in any of the middle three places.
The other two places can be filled in 9 ways (all digits from 0 to 9, except 9)
6 3 5 _ 9 9 4
Total Number of ways = 3 * 4 * 9 * 9 = 972 ways
Case 1: Last digit is 9.
So the last digit can be filled only in 1 way.
The remaining digits can be filled in 9 ways (all digits from 0 to 9, except 9)
6 3 5 9 9 9 1
Total Number of ways = 9 * 9 * 9 = 729 ways
Total number of ways = 729 + 972 = 1701 ways.
The same number of combinations would also apply for
6 7 54 _ _ _ _
Total number of possible combinations = 1701 * 2 = 3402.
IMO B
P.S - Looking at the number of possible combinations, it is likely that the person will be stranded for some more time
29 Dec 2021, 13:28
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Bunuel
Breaking Down the Info:
We have to select the last four digits for this telephone number, once we find out how many options there are we multiply by 2 since the first three digits have two options.
If the 9 is in any of the first three digits, then we have to fill in two digits and an odd number, each of which cannot be 9. That would be 9*9*4 options. Since the 9 can go in three slots, we multiply that by 3 to get 9*9*12.
If the 9 is the last digit, then we can fill in anything for the rest of the three digits except 9. That would be 9*9*9 options.
Add those up to get \(9*9*21\), and finally multiply by 2 since we had two options for the first three digits to get \(81*42 = (80 + 1)(40 + 2) = 3200 + 160 + 40 + 2 = 3402\). (We can immediately choose B as soon as we see the last digit must be 2).
Answer: B
