The only gift certificates that a certain store sold . . .

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 am; Followed by:3 members

The only gift certificates that a certain store sold . . .

by VJesus12 » Thu Nov 23, 2017 7:09 am

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The only gift certificates that a certain store sold yesterday were worth either $100 each or $10 each. If the store sold a total of 20 gift certificates yesterday, how many gift certificates worth $10 each did the store sell yesterday?

(1) The gift certificates sold by the store yesterday were worth a total of between $1,650 and $1,800.
(2) Yesterday the store sold more than 15 gift certificates worth $100 each.

The OA is A .

I am a little confuse here. Experts, may you clarify how to solve this DS question? I would be thankful.

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Source: Beat The GMAT — Data Sufficiency | Thu Nov 23, 2017 7:09 am

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Fri Nov 24, 2017 10:44 am

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Hi VJesus12,

We're told that the only gift certificates that a certain store sold yesterday were worth either $100 each or $10 each and that the store sold a total of 20 gift certificates. We're asked for the number of gift certificates worth $10 each that the store sold yesterday.

To start, it's worth noting that there's a pattern that you can take advantage of. Since we know that there were only 20 gift certificates sold, the total value of the certificates will change by a consistent amount as you increase the number of $100 certificates or the number of $10 certificates. For example:
0 $10s and 20 $100s = $2000
1 $10s and 19 $100 = $1910
2 $10s and 18 $100s = $1820
3 $10s and 17 $100s = $1730
Etc.

Notice that the decrease in the total value is consistently $90 less as you increase the number of $10 certificates by 1. You can use that pattern to your advantage....

1) The gift certificates sold by the store yesterday were worth a total of between $1,650 and $1,800.

IF... we have...
2 $10s and 18 $100s = $1820
3 $10s and 17 $100s = $1730
4 $10s and 16 $100s = $1640
There's ONLY ONE value that fits the information in Fact 1: (3 $10s and 17 $100s), so the answer to the question is 3.
Fact 1 is SUFFICIENT

2) Yesterday the store sold more than 15 gift certificates worth $100 each.

IF... we have...
2 $10s and 18 $100s = $1820 and the answer to the question is 2
3 $10s and 17 $100s = $1730 and the answer to the question is 3
Fact 2 is INSUFFICIENT

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]