ISEE Middle Level Quantitative : Numbers and Operations
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All ISEE Middle Level Quantitative Resources
Example Questions
Example Question #261 : Numbers And Operations
Round to the nearest thousandth.
Remember that for percentages, the key to setting up the problem is intelligent translation. The word "is" becomes 
Therefore, we can translate:
As...
To solve, divide both sides by 
Rounded, this is:
Example Question #41 : Percentage
500 is 
of the number.
The question becomes equivalent to asking this - 500 is 
We can find out by dividing 500 by 
Example Question #41 : Percentage
Using the information given in each question, compare the quantity in Column A to the quantity in Column B.
Jack scores a 40 on his first test and improves his score by 80% on his second test. Jill scores 50 on her first test, and her second test is 130% of her first test.
Column A Column B
Jack's 2nd Jill's 2nd
test score test score
The two quantities are equal.
The quantity in Column A is greater.
The quantity in Column B is greater.
The relationship cannot be determined from the information given.
The quantity in Column A is greater.
Jack improves by 80%, so we multiply his original score by 1.8 (the 1 to represent his earlier score and the .8 to add on his improvement). 40% times 1.8 equals 72%.
Jill's second test is 130% of her first test (that is, a 30% improvement). To find her new score we multiply her first score by 1.3. 50% times 1.3 equals 65%.
Thus, Jack's second test score is higher.
Example Question #263 : Numbers And Operations
Which is the greater quantity?
(a)
(b)
(b) is greater
(a) is greater
(a) and (b) are equal
It is impossible to tell from the information given
(b) is greater
No calculation is necessary. The whole in (b) is less, so 1 is a greater portion of that whole than the whole in (a). This makes (b) greater.
Example Question #42 : Percentage
Which is the greater quantity?
(a)
(b)
(a) and (b) are equal
It is impossible to tell from the information given
(a) is greater
(b) is greater
(a) is greater
Example Question #43 : Percentage
1,111 is 
999 is 
Which is the greater quantity?
(a)
(b)
(a) is greater
(b) is greater
(a) and (b) are equal
It is impossible to tell from the information given
(a) is greater
No calculation is necessary. In (a), the part is greater than the whole, so the percent 
Example Question #44 : Percentage
There were 48 pieces of fruit brought to the brunch. Twelve of the pieces of fruit were bananas. What percentage of the fruit were bananas?
50%
12%
66%
48%
25%
25%
Percentage involves part over whole. The total number of fruit was 48. The number of bananas was 12. Therefore, you can make a fraction from those numbers: 
Example Question #6 : How To Find Percentage
70% of 4,000 is equal to what percent of 6,400?
70% of 4,000 is equal to 
Evaluate:
The correct response is
Example Question #7 : How To Find Percentage
(A) 70% of 40% of
(B) 40% of 70% of
(A) and (B) are equal
(A) is greater
(B) is greater
It is impossible to determine which is greater from the information given
(A) and (B) are equal
40% of a number is the number multplied by 0.40; 70% of the number is the number multiplied by 0.70.
40% of 
70% of 
Regardless of the value of 
Example Question #3 : How To Find Percentage
(A) 25% of
(B) 50% of
(B) is greater
It is impossible to determine which is greater from the information given
(A) and (B) are equal
(A) is greater
It is impossible to determine which is greater from the information given
The greater of the two can be shown to depend on the value of 
Example 1:
Then 25% of 
and 50% of 
This makes (A) greater.
Example 2:
Then 25% of 
and 50% of 
This makes (B) greater.
Therefore, insufficient information is given in the problem to determine which is the greater.
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All ISEE Middle Level Quantitative Resources
