Magician Monster Hunt #1 (25/26)

Seven more than twice what number equals thirty-five?

• 14

• 15

• 16

• 17

Answer explanation

If the result is 35 when you double the number and add seven, we will start by subtracting 7 from 35 to get 28. So, our number is half of 28, which is 14. To solve algebraically, we first let n represent our unknown. Then we have 2n + 7 = 35. Subtracting 7 from each side yields 2n = 28. Then we divide each side by 2 to get n = 14.

If x is 3 more than y, and y is 5 less than z, then what is z - x?

• 2

• 5

• 8

• 10

Answer explanation

We are told that x = y + 3 and y = z − 5, which can be rewritten as y + 5 = z. We are asked to determine the value of z − x. Substituting we get (y + 5) − (y + 3) = y + 5 − y − 3 = 5 − 3 = 2.

My sister and I are buying a TV for $299. I will pay $45 more than my sister. How much does my sister pay?

• $127

• $129

• $132

• $136

Answer explanation

We are told that the television costs $299 and the older sibling will pay $45 more than the younger sibling. That means that the other 299 − 45 = 254 dollars will be split equally between the two siblings. Therefore, the younger sibling will pay 254 ÷ 2 = 127 dollars.

Tags

CCSS.3.OA.D.8

Kevin, Cindi, and Marcus have 1020 widgets. Marcus has half as many as Cindi. Kevin has 219. How many does Cindi have?

• 267

• 401

• 534

• 801

Answer explanation

See (Turning Word Problems Into Algebra Video) for steps.

Tags

CCSS.4.OA.A.3

A fraction increases by 1 when the numerator increases by 6. If the denominator increases by 36, it decreases by 1. What is the original fraction?

• 3/5

• 4/6

• 5/7

• 6/9

Answer explanation

Let the fraction be x/y. From the conditions, (x+6)/y = x/y + 1 and x/(y+36) = x/y - 1. Solving these gives x = 3 and y = 5, so the original fraction is 3/5.

Tags

CCSS.5.NF.B.5B

Douglas writes down his favorite number, which is a two-digit positive integer. He then turns the number into a three-digit number by writing a 7 at the end of his favorite number. This new number is 385 more than Douglass favorite number. What is Douglass favorite number?

• 42

• 63

• 53

• 65

Answer explanation

This problem can be solved several ways. First let’s solve it algebraically. We are told that Douglas’ favorite number is a positive two-digit integer; let’s call it AB where A is the tens digit and B is the units digit. That means that the value of his favorite number is 10A + B. Then a new number is created, AB7, where A now is the hundreds digit, B now is the tens digit and 7 is the units digit. The value of the new number is 100A + 10B + 7. Finally, we are told that the new number is 385 more than Douglas’ favorite number. So we have 100A + 10B + 7 = 10A + B +385. Subtracting 10A, B and 7 from both sides yields 90A + 9B = 378. Dividing both sides by 9 gives us 10A + B = 42. This is Doug’s favorite number.

Tags

CCSS.3.OA.D.8

A pound has pit bulls, chihuahuas, and mutts. All but 23 are pit bulls, all but 17 are chihuahuas, all but 28 are mutts. How many dogs total?

• 31

• 34

• 35

• 36

Answer explanation

Let p represent the number of pit bulls, c is the number of chihuahuas and m is the number of mutts. The second sentence of the problem yields the following equations, where A is the total number of dogs: p = A − 23, c = A − 17, m = A − 28 and A = p + c + m. If we add the first three equations we get p + c + m = 3A − 68. Substituting, we get A = 3A − 68. We now solve to determine that the total number of dogs at the pound is 2A = 68 → A = 34 dogs.

Tags

CCSS.6.EE.B.7

Largest integer whose square is less than 1,000,000?

• 999

• 1000

• 1001

• 1023

Answer explanation

One million is 1,000,000. Granted, we’re not supposed to be writing anything, but just looking at this, I can see that 1,000,000 = 10002, so the square of 999 (or 9992) would be the largest square less than one million.

Tags

CCSS.8.EE.A.2

What is the least positive three-digit integer that leaves a remainder of 1 when divided by 7.

• 100

• 106

• 105

• 107

Answer explanation

This means we need the smallest positive three-digit integer that is 1 more than a multiple of 7. Let’s build our smallest positive three-digit multiple of 7... it must be of the form 10_. Dividing 10 by 7 leaves a remainder of 3, and then making the units digit a 5 would make the situation such that 7 now evenly divides into 35. So 105 is the smallest positive three-digit multiple of 7 and 106 is the answer to the original question. (You may have gone a different route... many of us know 77 is a multiple of 7; and if we continue to add 7 or multiples of 7 we can find the number we’re looking for. Adding 21 to 77 gives us 98, so 99 would give us a remainder of 1, but isn’t a three-digit number; and then adding 7 more we get 106, so this is the smallest positive three-digit integer that is one more than a multiple of 7.)

Tags

CCSS.4.NBT.B.6

What is the least positive four-digit integer that leaves a remainder of 5 when divided by 9?

• 1004

• 1005

• 1007

• 1013

Answer explanation

I know 999 is a multiple of 9, and that’s pretty close to a four-digit number. In fact, if we add 5, we get 1004, and we know that 1004 will leave a remainder of 5 when it’s divided by 9, so this is our answer.