How to find the answer from a table - ISEE Middle Level Quantitative Reasoning
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Choose the best answer from the four choices given.
Katie wants to buy as many umbrellas as she can to give to her friends as Christmas gifts. She finds a deal online where she can get umbrellas for $7 each or four umbrellas for $25 (including tax). If shipping is $3 for every $20 of merchandise (or portion thereof), how many umbrellas can she buy if she has $140?
Choose the best answer from the four choices given.
Katie wants to buy as many umbrellas as she can to give to her friends as Christmas gifts. She finds a deal online where she can get umbrellas for $7 each or four umbrellas for $25 (including tax). If shipping is $3 for every $20 of merchandise (or portion thereof), how many umbrellas can she buy if she has $140?
The quickest way to solve this problem is by making a chart showing the units purchased and the total cost. Start with the 4-packs of umbrellas:
4-packs cost shipping cost total cost
1 $25 $6 $31
2 $50 $9 $59
3 $75 $12 $87
4 $100 $15 $115
5 $125 $21 $146 (too high)
Having determined that Katie can buy four of the 4-packs of umbrellas, now we see how many of the $7 individual umbrellas she can add to her order.
four 4-packs indiv. indiv. $ subtotal shipping $ total $
$100 1 $7 $107 $18 $125
$100 2 $14 $114 $18 $132
$100 3 $21 $121 $21 $142 (too high)
Therefore, Katie can buy (4) 4-packs and (2) individual umbrellas (18 total umbrellas) for $132.
ALTERNATIVELY, you can begin by determining the highest subtotal she can afford and work backwards from there. $120 is 6 x $20, so the shipping charge would be $6 x 3 = $18, for a total cost of $138. One more dollar on the subtotal would bring it into the next $20 segment, bringing the shipping charge up to $21 (and $142 is greater than $140). Thus, from here you could figure out the maximum number of $25 4-packs and $7 individual umbrellas Katie could buy with $120.
Since $6 is not enough to buy any umbrellas, the total would be
The quickest way to solve this problem is by making a chart showing the units purchased and the total cost. Start with the 4-packs of umbrellas:
4-packs cost shipping cost total cost
1 $25 $6 $31
2 $50 $9 $59
3 $75 $12 $87
4 $100 $15 $115
5 $125 $21 $146 (too high)
Having determined that Katie can buy four of the 4-packs of umbrellas, now we see how many of the $7 individual umbrellas she can add to her order.
four 4-packs indiv. indiv. $ subtotal shipping $ total $
$100 1 $7 $107 $18 $125
$100 2 $14 $114 $18 $132
$100 3 $21 $121 $21 $142 (too high)
Therefore, Katie can buy (4) 4-packs and (2) individual umbrellas (18 total umbrellas) for $132.
ALTERNATIVELY, you can begin by determining the highest subtotal she can afford and work backwards from there. $120 is 6 x $20, so the shipping charge would be $6 x 3 = $18, for a total cost of $138. One more dollar on the subtotal would bring it into the next $20 segment, bringing the shipping charge up to $21 (and $142 is greater than $140). Thus, from here you could figure out the maximum number of $25 4-packs and $7 individual umbrellas Katie could buy with $120.
Since $6 is not enough to buy any umbrellas, the total would be
Compare your answer with the correct one above
The table below gives the population of Buchanan City in each census year from 1930 to 1980.
Which is the greater quantity?
(a) The decline in the population of Buchanan City between 1940 and 1950
(b) The growth in the population of Buchanan City between 1950 and 1960
The table below gives the population of Buchanan City in each census year from 1930 to 1980.
Which is the greater quantity?
(a) The decline in the population of Buchanan City between 1940 and 1950
(b) The growth in the population of Buchanan City between 1950 and 1960
The population of Buchanan City in 1960 is greater than it was in 1940, so its decline between 1940 and 1950 must be less than its growth between 1950 and 1960.
The population of Buchanan City in 1960 is greater than it was in 1940, so its decline between 1940 and 1950 must be less than its growth between 1950 and 1960.
Compare your answer with the correct one above
The table below gives the population of Buchanan City in each census year from 1930 to 1980.
Which is the greater quantity?
(a) The population of Buchanan City in 1965
(b) The population of Buchanan City in 1975
The table below gives the population of Buchanan City in each census year from 1930 to 1980.
Which is the greater quantity?
(a) The population of Buchanan City in 1965
(b) The population of Buchanan City in 1975
No information about the population of Buchanan City is given for either 1965 or 1975.
No information about the population of Buchanan City is given for either 1965 or 1975.
Compare your answer with the correct one above
The table below gives the population of Buchanan City in each census year from 1930 to 1980.
Which is the greater quantity?
(a) The growth in the population of Buchanan City between 1930 and 1940
(b) The growth in the population of Buchanan City between 1950 and 1960
The table below gives the population of Buchanan City in each census year from 1930 to 1980.
Which is the greater quantity?
(a) The growth in the population of Buchanan City between 1930 and 1940
(b) The growth in the population of Buchanan City between 1950 and 1960
(a) Between 1930 and 1940, the population grew by 
(b) Between 1950 and 1960, the population grew by 
.
This makes (b) greater
(a) Between 1930 and 1940, the population grew by
(b) Between 1950 and 1960, the population grew by
This makes (b) greater
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The table below gives the population of Buchanan City in each census year from 1930 to 1980.
The population figures are not available for 1990, 2000, or 2010, but it is known that the population has increased by at least 300 over each ten-year period since 1980.
Which is the greater quantity?
(a) The population of Buchanan City in 2010
(b) 
The table below gives the population of Buchanan City in each census year from 1930 to 1980.
The population figures are not available for 1990, 2000, or 2010, but it is known that the population has increased by at least 300 over each ten-year period since 1980.
Which is the greater quantity?
(a) The population of Buchanan City in 2010
(b)
Since the population of Buchanan City increased by at least 300 over each of three decades since 1980, then the population in 2010 is at least
.
Since the population of Buchanan City increased by at least 300 over each of three decades since 1980, then the population in 2010 is at least
Compare your answer with the correct one above
The table below gives the population of Buchanan City in each census year from 1930 to 1980.
The population figures are not available for 1990, 2000, or 2010, but it is known that the population has not decreased since 1980.
Which is the greater quantity?
(a) The population of Buchanan City in 2010
(b) 
The table below gives the population of Buchanan City in each census year from 1930 to 1980.
The population figures are not available for 1990, 2000, or 2010, but it is known that the population has not decreased since 1980.
Which is the greater quantity?
(a) The population of Buchanan City in 2010
(b)
Since the population has not decreased since 1980, it can be inferred that the population in 2010 was greater than or equal to that in 1980, which is 4,275. However, nothing more is known.
Since the population has not decreased since 1980, it can be inferred that the population in 2010 was greater than or equal to that in 1980, which is 4,275. However, nothing more is known.
Compare your answer with the correct one above
The table below gives the population of Buchanan City in each census year from 1930 to 1980.
In 1930, 81% of the population of Buchanan City was non-White; in 1980, 61% was non-White.
Which is the greater quantity?
(a) The number of non-Whites living in Buchanan City in 1930
(b) The number of non-Whites living in Buchanan City in 1980
The table below gives the population of Buchanan City in each census year from 1930 to 1980.
In 1930, 81% of the population of Buchanan City was non-White; in 1980, 61% was non-White.
Which is the greater quantity?
(a) The number of non-Whites living in Buchanan City in 1930
(b) The number of non-Whites living in Buchanan City in 1980
(a) 81% of 2,984 is 
(b) 61% of 4,275 is 
(b) is greater
(a) 81% of 2,984 is
(b) 61% of 4,275 is
(b) is greater
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Use the chart below to answer the question.
How many students in Mr. Ray's class have a pet?
Use the chart below to answer the question.
How many students in Mr. Ray's class have a pet?
Each square represents 
students. Mr. Ray's bar has 
squares in it. That means we can take 
to find our total.
Each square represents
Compare your answer with the correct one above
Use the chart below to answer the question.
How many students in Ms. Smith's class have a pet?
Use the chart below to answer the question.
How many students in Ms. Smith's class have a pet?
Each square represents 
students. Ms. Smith's bar has 
squares in it. That means we can take 
to find our total.
Each square represents
Compare your answer with the correct one above
Use the chart below to answer the question.
How many students in Ms. Hen's class have a pet?
Use the chart below to answer the question.
How many students in Ms. Hen's class have a pet?
Each square represents 
students. Ms. Hen's bar has 2 squares in it. That means we can take 
to find our total.
Each square represents
Compare your answer with the correct one above
Use the chart below to answer the question.
How many students in Ms. Miller's class have a pet?
Use the chart below to answer the question.
How many students in Ms. Miller's class have a pet?
Each square represents 
students. Ms. Miller's bar has 
squares in it. That means we can take 
to find our total.
Each square represents
Compare your answer with the correct one above
Use the chart below to answer the question.
How many more students have a pet in Mr. Ray's class than Ms. Hen's class?
Use the chart below to answer the question.
How many more students have a pet in Mr. Ray's class than Ms. Hen's class?
Each square represents 
students. Mr. Ray's bar has 
squares in it, which means he has 
students with pets (
). Ms. Hen's bar has 
squares in it, which means she has 
students with pets (
).
To find the difference we subtract.
Each square represents
To find the difference we subtract.
Compare your answer with the correct one above
Use the chart below to answer the question.
How many more students have a pet in Mr. Ray's class than Ms. Miller's class?
Use the chart below to answer the question.
How many more students have a pet in Mr. Ray's class than Ms. Miller's class?
Each square represents 
students. Mr. Ray's bar has 
squares in it, which means he has 
students with pets (
). Ms. Milers bar has 
squares in it, which means she has 
students with pets (
).
To find the difference we subtract.
Each square represents
To find the difference we subtract.
Compare your answer with the correct one above
Use the chart below to answer the question.
How many more students have a pet in Ms. Smith's class than Mr. Ray's class?
Use the chart below to answer the question.
How many more students have a pet in Ms. Smith's class than Mr. Ray's class?
Each square represents 
students. Ms. Smith's bar has 
squares in it, which means she has 
students with pets (
). Mr. Ray's bar has 
squares in it, which means he has 
students with pets (
).
To find the difference we subtract.
Each square represents
To find the difference we subtract.
Compare your answer with the correct one above
Use the chart below to answer the question.
How many more students have a pet in Ms. Smith's class than Ms. Hen's class?
Use the chart below to answer the question.
How many more students have a pet in Ms. Smith's class than Ms. Hen's class?
Each square represents 
students. Ms. Smith's bar has 
squares in it, which means she has 
students with pets (
). Ms. Hen's bar has 
squares in it, which means she has 
students with pets (
).
To find the difference we subtract.
Each square represents
To find the difference we subtract.
Compare your answer with the correct one above
Use the chart below to answer the question.
How many more students have a pet in Ms. Smith's class than Ms. Miller's class?
Use the chart below to answer the question.
How many more students have a pet in Ms. Smith's class than Ms. Miller's class?
Each square represents 
students. Ms. Smith's bar has 
squares in it, which means she has 
students with pets (
). Ms. Miller's bar has 
squares in it, which means she has 
students with pets (
).
To find the difference we subtract.
Each square represents
To find the difference we subtract.
Compare your answer with the correct one above
Use the chart below to answer the question.
How many more students have a pet in Ms. Miller's class than Ms. Hen's class?
Use the chart below to answer the question.
How many more students have a pet in Ms. Miller's class than Ms. Hen's class?
Each square represents 
students. Ms. Miller's bar has 
squares in it, which means she has 
students with pets (
). Ms. Hen's bar has 
squares in it, which means she has 
students with pets (
).
To find the difference we subtract.
Each square represents
To find the difference we subtract.
Compare your answer with the correct one above
Use the chart below to answer the question.
How many students have pets in Mr. Ray's class and Ms. Hen's class?
Use the chart below to answer the question.
How many students have pets in Mr. Ray's class and Ms. Hen's class?
Each square represents 
students. Mr. Ray's bar has 
squares in it, which means he has 
students with pets (
). Ms. Hen's bar has 
squares in it, which means she has 
students with pets (
).
To find the total in both classes we add.
Each square represents
To find the total in both classes we add.
Compare your answer with the correct one above
Use the chart below to answer the question.
How many students have pets in Ms. Smith's class and Ms. Hen's class?
Use the chart below to answer the question.
How many students have pets in Ms. Smith's class and Ms. Hen's class?
Each square represents 
students. Ms. Smith's bar has 
squares in it, which means she has 
students with pets (
). Ms. Hen's bar has 
squares in it, which means she has 
students with pets (
).
To find the total in both classes we add.
Each square represents
To find the total in both classes we add.
Compare your answer with the correct one above
Use the chart below to answer the question.
How many students in first grade have a sibling?
Use the chart below to answer the question.
How many students in first grade have a sibling?
Each square represents 
students. The first grade bar has 
squares in it. That means we can take 
to find our total.
Each square represents
Compare your answer with the correct one above