Digital SAT Math Practice #3

For how many positive integers, a, is it true that a² ≤ 2a?

• None

• 1

• 2

• More than 2

Answer explanation

Since a is positive, divide both sides of the given inequality by a:

a² ≤ 2a ⇒ a ≤ 2 ⇒ a = 1 or 2

There are two positive integers that satisfy the given inequality.

• I only

• II only

• I and II only

• I and II and III

Tags

CCSS.HSN.RN.B.3

• I only

• II only

• III only

• II and III only

Tags

CCSS.6.NS.C.7A

CCSS.6.NS.C.7B

At 3:00 A.M. the temperature was 13° below zero. By noon it had risen to 32°. What was the average hourly increase in temperature?

Answer explanation

In the 9 hours from 3:00 A.M. to noon, the temperature rose 32 - (- 13) = 32 + 13 = 45°. Therefore, the average hourly increase was 45 ÷ 9 = 5°.

Tags

CCSS.7.EE.B.3

• c - a - b

• a + b - c

• c - ab

Tags

CCSS.8.EE.A.1

If p and q are primes greater than 2, which of the following must be true?
I. p + q is even.
II. pq is odd.
III. p² - q² is even

• I only

• I and II only

• I and III only

• I, II and III

Answer explanation

+) All primes greater than 2 are odd, so p and q are odd, and p + q is even. (I is true.)

+) The product of two odd numbers is odd. (II is true.)

+) Since p and q are odd, so are their squares, and so the difference of the squares is even. (III is true.)

Tags

CCSS.6.EE.A.1

At Cathy's Candy Shop, 25.5 pounds of chocolate are being divided into gift boxes, each containing 100 grams of chocolate. To the nearest tenth, how many ounces of chocolate will be left over when there isn't enough chocolate to fill another whole box?

(1 pound = 16 ounces, and 1 pound = 454 grams)

Answer explanation

25.5 pounds of chocolate weighs 25.5 × 454 = 11,577 grams.

Since 11,577 ÷ 100 = 115.77, there is enough chocolate to make 115 gift boxes and have 0.77 × 100 = 77 grams left over.

Since 1 pound = 454 grams, 1 ounce = 454 ÷ 16 = 28.375 grams.

Finally, 77 ÷ 28.375 = 2.714. To the nearest tenth, there will be 2.7 ounces of chocolate left over.

Tags

CCSS.5.MD.A.1

Maria has two electronic beepers. One of them beeps every 4 seconds; the other beeps every 9 seconds. If they are turned on at exactly the same time, how many times during the next hour will both beepers beep at the same time?

Answer explanation

Since 36 is the LCM of 4 and 9, the beepers will beep together every 36 seconds. One hour = 60 minutes = 3600 seconds, and so the simultaneous beeping will occur 100 times

If - 7 ≤ x ≤ 7 and 0 ≤ y ≤ 12, what is the greatest possible value of y - x?

Answer explanation

To make y - x as large as possible, let y be as large as possible (12), and subtract the smallest amount possible (x = -7):

12 - (-7) = 19.

If x is an integer less than 1000 that has a remainder of 1 when it is divided by 2, 3, 4, 5, 6, or 7, what is one possible value of x?

Answer explanation

The LCM of 2, 3, 4, 5, 6, 7 is 420, so 420 is divisible by each of these integers, and there will be a remainder of 1 when 421 is divided by any of them. One more than any multiple of 420 will also work.

Tags

CCSS.8.EE.C.7B