HSPT Math : Problem Solving
Study concepts, example questions & explanations for HSPT Math
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Example Questions
Example Question #1 : Problem Solving
Jenny is getting ready for school. She bought school supplies on a tax-free day. She bought notebooks for $1.25 each and crayons for $0.90 each. Jenny bought two more notebooks than crayons. She paid with a ten dollar bill and got $1.05 in change. How many notebooks did she buy?
5
3
2
4
1
5
Define variables as x = number of crayons and x + 2 = number of notebooks
To find out how much she spent, we subtract her change from what she paid with: 10.00 – 1.05 = 8.95
Then we need to solve the problem cost of notebooks plus the cost of crayons equals the total cost.
1.25(x + 2) + 0.90x = 8.95 and solving for x gives 3 crayons and 5 notebooks
Example Question #2 : Problem Solving
A runner runs 10.2 miles east, then 2.3 miles west, then 1.4 miles east.
How many miles did the runner travel from where he started? (How far east did the runner go)?
6.5 miles
10.2 miles
19.3 miles
13.9 miles
9.3 miles
9.3 miles
When the runner is travelling east, it's in the positive direction. West is the negative direction. So we can compute it by doing the operation 10.2 + (–2.3) + 1.4 = 9.3
Example Question #3 : Problem Solving
If Susie bought a pair of shoes for 
You add all three values and you get 
Example Question #4 : Problem Solving
What is 
Example Question #5 : Problem Solving
Subtract:
Rewrite 
Example Question #1 : Fluently Add, Subtract, Multiply, And Divide Multi Digit Decimals: Ccss.Math.Content.6.Ns.B.3
Define an operation 
If 
If 
Of the other three factors, it can be seen that the GCF of 20 and each individual number is 10 by looking at each prime factorization:
In each pairing, the common prime factors are 2 and 5, so the GCF is 
Example Question #6 : Problem Solving
The above is a menu at the concession stand at a drive-in movie.
Gary wants to order two hamburgers and two small orders of fries. He wants to order two sodas of the same size. If he has just a twenty-dollar bill on hand, what is the largest size soda of which he can order two?
Gary can afford two medium sodas, but not two large sodas
Gary can afford two large sodas
Gary cannot afford two sodas
Gary can afford two small sodas, but not two medium or large sodas
Gary can afford two large sodas
The easiest way to think of this is to note that Gary seems to be ordering for two people, himself and a friend. He has $20, so half of this will be for himself and half for his friend - and half of $20 is $10.
Each hamburger costs $4.89, and each small order of fries costs $2.29. This leaves
to spend on a soda for each person. This will enable to him to buy both himself and his friend a large soda.
Example Question #3 : Arithmetic
The above is a menu at the concession stand at a drive-in movie. The stand also offers a Family Chicken Strip Bucket - twenty chicken strips, four medium orders of fries, and four medium sodas for $30.
How much more would the items of the Family Chicken Strip Bucket cost if they were purchased separately?
(Ignore tax)
There are twenty chicken strips in the Family Chicken Strip Bucket, which are the same as in five orders; each order costs $3.99 separately. Each medium order of fries costs $2.79 separately, and each medium soda costs $1.69 separately. The items separately cost a total of
Subtract $30; the savings amount to
Example Question #4 : Subtracting Multi Digit Decimals
The above is a menu at the concession stand at a drive-in movie. The stand also offers a special "Meal Deal": a hamburger or a hot dog, a medium order of fries, and a medium soda for 
Randy orders two Meal Deals - a hamburger Meal Deal for himself and a hot dog Meal Deal for his friend Denise. How much more would he have paid for the items separately?
(Ignore tax)
The two Meal Deals cost 
Purchased separately, the hamburger would have cost $4.89; the hot dog, $4.39; each of the two medium orders of fries, $2.79; and each of the two medium sodas, $1.69. The total price of the items, purchased separately, would have been
The difference between this and the $16 paid for the food is
Example Question #6 : Decimals
Above is the menu at the concession stand at a school carnival. Ken wants to purchase a hamburger, a medium order of fries, and medium soda for himself, and a hot dog, a small order of fries, and a small soda for his friend Donna. He hands the clerk a $10 bill and a $5 bill. He has some $1 bills in his pocket; how many of them will he need to hand to the clerk along with the other two bills?
(No tax is charged, since this is a school event)
Two
One
Three
None
Three
The items Ken purchases are as follows:
Hamburger: $4.89
Medium fries: $2.79
Medium soda: $1.69
Hot dog: $4.39
Small fries: $2.29
Small soda: $1.09
The sum of the prices of these items:
Subtract from $20:
Rounding this up - Ken needs to give the clerk three more $1 bills.
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