a small soda

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 am; Location: India; Thanked: 267 times; Followed by:80 members; GMAT Score:760

a small soda

by sanju09 » Sat Apr 04, 2009 5:02 am

At a snack bar, a customer who orders a small soda gets a cup containing c ounces of soda, where c is at least 12 but no more than 12 ½. Which of the following describes all possible values of c?
A. │12 ½ - c│ ≤ ½
B. │c - 12│ ≤ ½
C. │c - 12│≤ ¼
D. │c – 12 ¼│ ≤ ½
E. │c – 12 ¼│ ≤ ¼

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Source: Beat The GMAT — Problem Solving | Sat Apr 04, 2009 5:02 am

scoobydooby: Legendary Member; Posts: 1035; Joined: Wed Aug 27, 2008 10:56 pm; Thanked: 104 times; Followed by:1 members

by scoobydooby » Sat Apr 04, 2009 5:59 am

given 12<c<12.5
we need to find which of the following translates to the above:

A. │12 ½ - c│ ≤ ½ = 0<│12 ½ - c│<1/2
=>-12.5<|-c|<12

B. │c - 12│ ≤ ½ =0<│c - 12│ ≤ ½
=>12<|c|<12.5 correct

hence B

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kapsii: Senior | Next Rank: 100 Posts; Posts: 38; Joined: Thu Feb 05, 2009 8:43 am; Thanked: 5 times

option B does not fit for other values of C.

by kapsii » Sat Apr 04, 2009 6:46 am

I think the answer is E

scoobydooby, when I tried to double check the option B, it still satisfies for c = 11.5, thus it cannot be the correct answer.

My reasoning: the absolute value function swings both ways along the number line, thus, ideally I would want to check with range/2, i.e. check with 1/4 instead of 1/2. So, reading the options, I had a hunch that E is the most probable, with next probable answer being D and so on, I checked the option E with the data provided and it satisfies the given conditions.

Cheers,
Dubes

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kapsii: Senior | Next Rank: 100 Posts; Posts: 38; Joined: Thu Feb 05, 2009 8:43 am; Thanked: 5 times

by kapsii » Sat Apr 04, 2009 6:55 am

scoobydooby, I think I found out where you went wrong...

B: |c - 12| ≤ ½
should convert to
-½ ≤ (c-12) ≤ ½
or (-½ + 12) ≤ c ≤ (½ + 12)

Similarly Option E │c – 12 ¼│ ≤ ¼
should be converted as:
-¼ ≤ (c – 12 ¼) ≤ ¼
or (-¼ + 12 ¼ )≤ c ≤ (¼ + 12 ¼)
which satisfies the inequality described in the question...

for more information on the absolute value function, the wiki provides more details (link given below)

https://en.wikipedia.org/wiki/Absolute_value

Cheers,
Dubes