Moderate# Lock Combinations

GMAT-XB3QBD

__Advertisement by Titan Padlock Company__

High school students love our padlocks for their gym lockers! Keep your clothes and valuables secure knowing that our locks

have 60 numbers! A three number combination with 60 choices per number makes it almost impossible for this padlock to be

compromised. The materials are precision made to high tolerance – within less than half of a number unit! No one will steal

your stuff!

__Letter to Titan Padlock Company by a High School Student__

I am writing to respectfully point out some major deficiencies in your padlocks. The chances of guessing the combination on

someone else’s lock is really small - 1 out of 216,000, since that is 60 x 60 x 60. However, the tolerance is much lower than

you claim. I found that even though my combination was 55-03-32, I was able to open it with a tolerance of two number units

on either side, like 53-05-34. I would figure then that any of the numbers 53, 54, 55, 56, or 57 would count the same as the

designed “55”, and thus there are five times fewer effective values per number than advertised. This greatly reduces the

number of possible combinations that are actually effective. I am worried that someone could systematically try all the

possible combinations in a relatively short time and break in to my swim locker without physically destroying the lock and

leaving any evidence.

__Letter from Titan Padlock Company to a High School Student__

We appreciate your feedback about our padlocks. The purpose of a lock is to deter and delay. Even with fewer possible

combinations, it would still take about 10 to 15 seconds per combination to try every possibility, and thus, it would take a

long time to break a lock, and it is likely a perpetrator would be caught acting suspiciously first. We assure you, however,

that under appropriate environmental conditions of temperature and humidity (often not satisfied near swimming pools),

that the tolerance is repeatedly tested not to be anywhere as high as two number units. If interested, please consult our

website for more security options, including our higher cost options that have additional internal pin chambers and key

cut depths.

Consider each of the following statements. Does the information in the emails support the inference as stated? Choose Yes if the statement can be accurately inferred; otherwise choose No.

Yes

No

Yes

No

If the tolerance is two number units as the student suggests, then there would be one-fifth as many possible combinations.

Yes

No

Titan Padlock Company takes full responsibility for the decreased tolerance that was observed by the high school student.

Yes

No

If the padlocks as advertised by the company had a three number combination in which no number could be used twice in a single combination, the advertised number of possible combinations would be reduced by at least 2%.