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by oquiella » Thu Dec 24, 2015 9:37 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 $1650 and $1800.
2. Yesterday the store sold more than 15 gift certificates worth $100 each.

Answer: A


Please explain why A is sufficient when there could have been a range between $1650 and $1800.
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by DavidG@VeritasPrep » Fri Dec 25, 2015 6:57 am

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oquiella wrote: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 $1650 and $1800.
2. Yesterday the store sold more than 15 gift certificates worth $100 each.

Answer: A


Please explain why A is sufficient when there could have been a range between $1650 and $1800.
The key here is to recognize that we have a total of 20 gift certificates and that the number of gift certificates of each type must be an integer value. Say the store sold 17 of $100 certificates and 3 of the $10. That would give us 17*100 + 3*10 = 1730. That's between 1650 and 1800, so that's one possible scenario.

Now let's see if anything else can work. What if there were 18 of the $100 certificates and 2 of the $10? That gives us a total of 1820 -not between 1650 and 1820 so this not a possibility that satisfies the statement.

What if there were 16 of the $100 certificates and 4 of the $10? That gives us a total of 1640 - not between 1650 and 1800, so we can't use this scenario either.

The only possibility that satisfies the statement is that there were 17 of the $100 certificates and 3 of the $10 certificates. So the answer is
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by DavidG@VeritasPrep » Fri Dec 25, 2015 7:04 am

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oquiella wrote: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 $1650 and $1800.
2. Yesterday the store sold more than 15 gift certificates worth $100 each.

Answer: A


Please explain why A is sufficient when there could have been a range between $1650 and $1800.
Algebraically, we can say that 'x' is the number of $10 certificates and '20-x' is the number of $100 certificates. (Because we know there are 20 total.) We know that 10x + 100(20-x) is the total value of the certificates. 10x + 100(20-x) = 10x + 2000 - 100x = 2000 - 90x. We know this value is between 1650 and 1800. Now test x's.

x = 1 --> 2000 - 90 = 1910. Nope
x = 2 --> 2000 - 180 = 1820. Nope
x=3 ---> 2000 - 270 = 1730. Satisfies!
x = 4 ---> 2000 - 360 = 1640. Nope

Only one value works, so we know that x = 3.
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by [email protected] » Sun Feb 18, 2018 8:32 pm

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Hi All,

We're told that the only gift certificates that a certain store sold yesterday were worth either $100 each or $10 each and the store sold a total of 20 gift certificates yesterday. We're asked for the number of gift certificates worth $10 each that the store sold yesterday. This question can be solved with a bit of 'brute force' and some basic arithmetic.

To start, since we have just 20 gift certificates, we can list out a few of the possibilities and look for a pattern.
There could be...
20 $10 certificates and 0 $100 certificates = (20)($10) + (0)($100) = $200
19 $10 certificates and 1 $100 certificates = (19)($10) + (1)($100) = $290
18 $10 certificates and 2 $100 certificates = (18)($10) + (2)($100) = $380
17 $10 certificates and 3 $100 certificates = (17)($10) + (3)($100) = $470

For every $10 certificate that is changed to a $100 certificate, the total value of the 20 certificates increases by $90 (and you can use this pattern to go 'in reverse' from 20 $100 certificates on down).

1) The gift certificates sold by the store yesterday were worth a total of between $1650 and $1800.

Based on the pattern defined above, the total could be...
$2000, $1910, $1820, $1730, $1640, etc.

Only one of these values is between $1650 and $1800 though - $1730 (3 $10s and 17 $100s).
Fact 1 is SUFFICIENT

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

With Fact 2, there are several possible outcomes, including $2000 (0 $10s and 20 $100s) and $1920 (1 $10 and 19 $100s).
Fact 2 is INSUFFICIENT

Final Answer: A

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Contact Rich at [email protected]
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by Jeff@TargetTestPrep » Tue May 29, 2018 4:58 pm

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oquiella wrote: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 $1650 and $1800.
2. Yesterday the store sold more than 15 gift certificates worth $100 each.
We can let h = the number $100 gift certificates sold and t = the number of $10 gift certificates sold. Thus, we have h + t = 20, and we need to determine the value of t.

Statement One Alone:

The gift certificates sold by the store yesterday were worth a total of between $1650 and $1800.

We see that number of $100 gift certificates sold is no more than 17. That is, h ≤ 17.

If h = 17, then t = 3, and the total value of the gift certificates is 17(100) + 10(3) = $1730, which is between $1650 and $1800.

If h = 16, then t = 4, and the total value of the gift certificates is 16(100) + 10(4) = $1640. However, this is between not $1650 and $1800. Also, we don't have to go any further down for the value of h, since we can see that from this point that there is no way the total value is between $1650 and $1800.

Therefore, we see that h must be 17 and t must be 3. Statement one alone is sufficient to answer the question.

Statement Two Alone:

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

We see that h > 15, so h could be 16, 17, 18, 19 or 20 and t could be 4, 3, 2, 1, or 0, respectively. Since we don't have a unique value for t, statement two alone is sufficient to answer the question.

Answer: A

Jeffrey Miller
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