SAT Data - Tables
To successfully solve problems with data tables on the SAT, you need to know how to interpret:
Contents
Examples
\[\begin{array}{|c|c|c|} \hline \text{Number of Eggs in a Carton} & \text{Price}\\ \hline 6 & $3.99\\ \hline 12 & $5.80\\ \hline 18 & $6.30\\ \hline \end{array}\]
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) \(\ \ 5.80\)
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.
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) \(\ \ $41.50\)
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).
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 \(=5\cdot $6.30 + 10\cdot $1.00 = $41.50.\)
\[\begin{array}{|c|c|c|c|c|} \hline & \text{High School} & \text{Middle School} & \text{ Total}\\ \hline \text{Boys} & a & 2b & X\\ \hline \text{Girls} & 2a & b & Y\\ \hline \text{Total} & M & N & T\\ \hline \end{array}\]
In the table above, each letter represents the number of students in that category. Which of the following equals \(M-N?\)
(A) \(\ \ X\)
(B) \(\ \ Y\)
(C) \(\ \ 3(Y-X)\)
(D) \(\ \ \frac{T}{3}\)
(E) \(\ \ X+Y\)
Review
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