A combination lock is set to open when the correct direction sequence

Question

A combination lock is set to open when the correct direction sequence is selected, either left-right-left or right- left-right, and when the correct three numbers from 1 to 60,inclusive,are selected in the correct order. If each number can be used only once, which of the following gives the number of different combinations that can be set to open the lock?

A. (30)(59)(58)
B. (60)(60)(60)
C. (60)(59)(58)
D. 2(60)(60)(60)
E. 2(60)(59)(58)

A. (30)(59)(58)
B. (60)(60)(60)
C. (60)(59)(58)
D. 2(60)(60)(60)
E. 2(60)(59)(58)

Archit3110 · Answer

from my understanding of the question the total ways possible will be one only because the lock shall open only when  correct direction sequence is selected , so only one possible way

60*59*58
option C

Bunuel  please check OA

Bunuel · Answer

_____________________________________
Fixed the OA.

abhishekmayank · Answer

I am confused. Whether correct combination here means only the combination of numbers an doesn't include the direction ?

Question is : either left-right-left  or  right- left-right,  and  when the correct three numbers from 1 to 60

If direction and sequence of 3 numbers both constitute a combination then we should factor the OR condition in the direction and the answer should be = 2*60*59*58

Kindly clarify..

turbosea · Answer

But what about the left-right-left and right-left-right? Wont there be 2 ways to reach a particular pattern?

vedha0 · Answer

there are 2 ways to reach a particular pattern but its still only 1 pattern. for example, 12-23-34 can be reached by keying in 12,23,34 from left to right. or using 34,23,12 from right to left. still the pattern in the same and we should only count once. so archit soln seems to be right.

sujoykrdatta · Answer

Say the code is 1-2-3. You need to get to 1 by rotating the dial left (clockwise) to reach 1, then right (counter clockwise) to reach 2 and then left to reach 3 OR the reverse, i.e. first right, then left and then right. 
Thus, even if someone selected the correct numbers, the person would still have to get the above sequence correct, else the lock won't open. 
For example, if someone uses the sequence L-L-L, it won't open. However, it is already known that the sequence is either L-R-L or R-L-R. Thus, while trying the sequence, someone would definitely use any one of those two. So, that information is redundant. 
Thus, essentially, it is only about the choice of the 3 numbers in the correct order i.e., 60 * 59 * 58 ways

Note: To understand better, say, we have to key-in a password using the letters C, A, T, and while making the input, we can either use all caps or all small, both would be counted as equivalent passwords. To count the number of options, we will simply say CAT, CTA, ACT, ATC, TAC, TCA. We won't count the other case of all small since that is anyways equivalent to these 6. Thus, the answer is simply 3 * 2 * 1 = 6

Answer C

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

A combination lock is set to open when the correct direction sequence

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A combination lock is set to open when the correct direction sequence

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards