SAT Data - Tables

To successfully solve problems with data tables on the SAT, you need to know how to interpret:

• data tables

$$\begin{array}{|c|c|c|} \hline \text{Number of Eggs in a Carton} & \text{Price}\\ \hline 6 & \$3.99\\ \hline 12 & \$5.80\\ \hline 18 & \$6.30\\ \hline \end{array}$$

Which of the following is the closest approximation of the price of 1 egg when buying a carton of 12?

(A) $\ \ 0.40$
(B) $\ \ 0.50$
(C) $\ \ 0.60$
(D) $\ \ 0.70$
(E) $\ \ 5.80$

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Correct Answer: B

Solution:

According to the table, a carton of 12 eggs costs $5.80. So, 1 egg costs $\frac{\$5.80}{12}=\$0.48.$ The best approximation is $0.50.

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Incorrect Choices:

(A)
This is approximately how much 1 egg costs when buying a carton of 18 eggs.

(D)
This is approximately how much 1 egg costs when buying a carton of 6 eggs.

(C)
This answer is just offered to confuse you.

(E)
This is how much a 12-egg carton costs. You must divide this by 12 in order to obtain the price of one egg in a 12-egg carton.

$$\begin{array}{|c|c|c|} \hline \text{Number of Eggs in a Carton} & \text{Price}\\ \hline 1 & \$1.00\\ \hline 6 & \$3.99\\ \hline 12 & \$5.80\\ \hline 18 & \$6.30\\ \hline \end{array}$$

What would be the least amount of money needed to purchase exactly 100 eggs?

(A) $\ \ \$31.50$
(B) $\ \ \$35.00$
(C) $\ \ \$39.49$
(D) $\ \ \$40.80$
(E) $\ \ \$41.50$

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Correct Answer: C

Solution:

1 egg in a 6-egg carton costs $3.99/6=$0.67, 1 egg in a 12-egg carton costs $5.80/12=$0.48, and 1 egg in an 18-egg carton costs $6.20/18= $0.35. Since the price per egg is lowest when purchasing 18-egg cartons, we should ideally buy as many of those as possible to reduce the cost.

18 doesn't divide 100 exactly. So we cannot purchase 100 eggs only with 18-egg cartons. The maximum 18-egg cartons we can purchase is 5:

5 cartons of 18, 1 carton of 6, and 4 single eggs $=5 \cdot \$6.30+1\cdot \$3.99 + 4\cdot \$1 = \$39.49.$

Clearly, the only other combination involving 5 cartons of 18 eggs will be more expensive:

5 cartons of 18 and 10 single eggs $=5\cdot \$6.30 + 10\cdot \$1 = \$41.50.$

What happens if we purchase four 18-egg cartons?

4 cartons of 18, 2 cartons of 12, and 3 single eggs $=4 \cdot \$6.30 + 2 \cdot \$5.80 + 3\cdot \$1 = \$39.80.$

And, substituting 6-egg cartons for the 12-egg cartons in this last combination will only increase the price since the price per egg in a 6-egg carton is higher than that in a 12-egg carton.

What about combinations with three 18-egg cartons? Let's say we could buy three 18-egg cartons, and let's also imagine we were able to buy all the remaining $100-3\cdot 18 = 46$ eggs at the price we would pay for an egg when buying 12-egg cartons, $0.48. Note that if we were able to do this, this would be the cheapest price involving three 18-egg cartons.

Then we would have to pay $3\cdot \$6.30 + 46 \cdot \$0.48 = \$40.98 > \$39.49.$

By analogous reasoning, we reject all other combinations involving three, two, one, or zero 18-egg cartons.

So, the correct answer is (C).

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Incorrect Choices:

(A)
This is the price of five 18-egg cartons, or 90 eggs each at $0.35. But, we need 100 eggs, not 90.

(B)
If we were to buy the hundred eggs at the cheapest rate of $\$0.35$ (1 egg in an 18-egg carton costs $0.35), we would get this wrong answer. The eggs are only sold as singles, in which case the price of one egg is $\$1.00$ or in cartons of 6, 12, or 18.

(D)
This is the combination of 4 cartons of 18, 2 cartons of 12, and 4 single eggs $=4 \cdot \$6.30 + 2 \cdot \$5.80 + 4\cdot \$1.00 = \$40.80$

(E)
This is the combination of 5 cartons of 18 eggs and 10 single eggs $=5\cdot \$6.30 + 10\cdot \$1.00 = \$41.50.$

If you thought these examples difficult and you need to review the material, these links will help:

• Data Tables
• Mean
• Median
• Mode
• Data Presentation Problem Solving

• SAT General Tips