DSAT extra practice Ch1 Lv1

1. Question

Emily sold [math]p[/math] lamb chops and [math]q[/math] steaks in her restaurant. The prices of a lamb chops and a steaks are $30 and $25 respectively. Which of the following expressions represents Emily’s revenue this Saturday?

[math]30p+25q[/math]
[math]30+p+25+q[/math]
[math]30p\cdot25q[/math]
[math](30+25)(p+q)[/math]

2. Question

According to the policy of Happy school, students need to acquire at least 160 course credits to graduate. Taking a required course grants 4 course credits and taking an elective course grants 2.5 course credits. Tristan is a senior. He has already gotten 120 course credits. Tristan has to take [math]x[/math] required courses and [math]y[/math] elective courses in his senior year, which of the following inequalities represent the restrictions of [math]x[/math] and [math]y[/math]?

[math]x+y\geq40[/math]
[math]4x+2.5y\geq40[/math]
[math]4x\geq40[/math] and [math]2.5y\geq40[/math]
[math]4x\geq20[/math] and [math]2.5y\geq20[/math]

3. Question

If cream frosted donuts are priced at $1.4 each, buying [math]x[/math] donuts would cost $[math]y[/math]. Which of the following equations correctly represent [math]y[/math]?

[math]1.4+x=y[/math]
[math]1.4-x=y[/math]
[math]1.4x=y[/math]
[math]1.4=xy[/math]

4. Question

A Hotel has 100 big rooms for 4-person families and 150 small rooms for couples. There are a total of 500 people that live in the hotel, represented by the equation [math]4x+2y=500[/math]. Which of the following best interprets the context of [math]y[/math]?

The number of small rooms used
The number of big rooms used
The number of rooms used
The number of 4-person family lived

5. Question

If [math]a=\dfrac{2b-6}{2}[/math], which of the following expressions is equivalent to [math]b[/math]?

[math]b=a+3[/math]
[math]b=a+6[/math]
[math]b=2a+6[/math]
[math]b=2(x+6)[/math]

6. Question

$$ab=2-ac$$What is the expression of [math]a[/math] in terms of [math]b[/math] and [math]c[/math]?

[math]a=\dfrac{2}{b}-c[/math]
[math]a=\dfrac{2}{b+c}[/math]
[math]a=\dfrac{2}{b}+\dfrac{2}{c}[/math]
[math]a=\dfrac{2}{b-c}[/math]

7. Question

$$5x-4(3-x)$$Which of the following expressions is equivalent to the expression above?

[math]6x-12[/math]
[math]4x-12[/math]
[math]x-12[/math]
[math]9x-12[/math]

8. Question

If [math]a+2b=10[/math], what is the value of [math]4a+6+8b[/math]?

9. Question

If [math]xy=4[/math], what is the value of [math](2x)(2y)-3[/math]?

10. Question

$$4x-12+7a=0$$If [math]x=-4[/math] is the solution to the equation, what is the value of [math]7a[/math]?

[math]4[/math]
[math]-4[/math]
[math]28[/math]
[math]-28[/math]

11. Question

$$40c+70a=800$$The equation above models the number of children, [math]c[/math], and the number of adults, [math]a[/math], an elevator can safely carry at any given time. If there are currently 4 adults in the elevator, how many more children can it carry?

[math]20[/math]
[math]15[/math]
[math]13[/math]
[math]0[/math]

12. Question

Tom was chasing Jerry because Jerry stole Tom s milk. Suppose the speeds of Tom and Jerry are 14m/s and 3m/s respectively. Given that Tom is 187 meters from Jerry, how long will it take until Tom catches Jerry?

11 seconds
13 seconds
14 seconds
17 seconds

13. Question

$$x-2x+3x-4x+5x=30$$What is the solution to the equation above?

14. Question

$$a(x+3)=2(x-b)$$If the equation above has infinite solutions, which of the following values cannot be [math]a+b[/math]?

[math]5[/math]
[math]1[/math]
[math]-1[/math]
[math]-5[/math]

15. Question

Luna can seat 5 dumplings within 8 minutes. If there are 18 dumplings in Luna’s lunch box, how much time does she need to finish his lunch?

28 minutes 0.8 seconds
28 minutes 8 seconds
28 minutes 48 seconds
28 minutes 52 seconds

16. Question

Which of the following expressions is equivalent to [math](-2ab^2c^{-3})^3[/math]?

[math]-\dfrac{8a^3b^6}{c^9}[/math]
[math]\dfrac{8a^3b^6}{c^9}[/math]
[math]-\dfrac{2ab^2}{c^9}[/math]
[math]\dfrac{2ab^2}{c^9}[/math]

17. Question

$$\frac{a^3b^{-4}}{a^{-5}b^6}$$Which of the following expressions is equivalent to the expression above?

[math]\dfrac{a^4}{b^5}[/math]
[math]\dfrac{a^8}{b^{10}}[/math]
[math]\dfrac{b^5}{a^4}[/math]
[math]\dfrac{b^{10}}{a^8}[/math]

18. Question

If [math]2^{x+2}=4^{y-3}[/math], which of the following relation between [math]x[/math] and [math]y[/math] is correct?

[math]x+2=2(y-3)[/math]
[math]x+2=\dfrac{1}{2}(y-3)[/math]
[math]x+2=\sqrt{y-3}[/math]
[math]x+2=(y-3)^2[/math]

19. Question

Which of the following expression is equal to [math]2^n+2^n[/math]?

[math]2^{2n}[/math]
[math]2^{n+1}[/math]
[math](2^n)^2[/math]
[math]2^{n^2}[/math]

20. Question

$$(2\cdot(-3)^{-2})^{-3}$$If the number above can be written as [math]a\cdot3^b[/math] where [math]a[/math] and [math]b[/math] are integers and [math]a<1[/math], what is the value of [math]ab[/math]?

[math]\dfrac{3}{4}[/math]
[math]-\dfrac{3}{4}[/math]
[math]\dfrac{729}{8}[/math]
[math]-\dfrac{729}{8}[/math]

21. Question

A 160 grams of a hamburger patty contains 48 grams of fat. If 1 gram of fat contains 9 kcal, how many calories does a 720 grams of a giant hamburger patty?

432 kcal
1944 kcal
5832 kcal
6480 kcal

22. Question

Ena had been saving towards a Lamborghini. Her annual salary is $13,200 and she saves 15% of it for the Lamborghini. How much money does Ena save each month?

23. Question

If making one standard caramel custard requires 7 grams of sugar, how many standard caramel custard can be made with 100 grams of sugar at most?

[math]12[/math]
[math]13[/math]
[math]14[/math]
[math]15[/math]

24. Question

Chris is a policeman. He sets a checkpoint on Happy Street to inspect for drunk driving every Sunday. Based on his experience, he will find 4 drunk drivers for every 15 drivers. Assume around 9,000 cars pass his checkpoint. How many fines will Chris issue?

25. Question

In the 2023 AP Stats exam, 15.1% of students scored a 5. With 242,929 students taking the exam that year, how many students scored a 5? Round to the nearest integer.

26. Question

According to FIFA, the length of a standard soccer field must be between 110 and 120 yards. Mr. Lin spent 1.2 billion to build a soccer field to host the 2026 World Cup. To make sure the size of the field satisfies the standard, Mr. Lin assigned an inspector to confirm the length. The inspector decided to measure the length of the field by walking. On average, the inspector walks 1.5 feet every step. If the inspector took 210 steps, what is the length, in yards, of the soccer field?

3 feet [math]=[/math] 1 yard

27. Question

Ms. Moose’s house has some leaky pipes. According to the water meter, Ms. Moose s water consumption this period is 48 degrees more than the previous period. One degree of water is equal to one kiloliter and every period is two months. On average, how many milliliters of water is leaked from Ms. Moose s pipes each day?

[math]800[/math]
[math]800,000[/math]
[math]1,600,000[/math]
[math]48,000,000[/math]

28. Question

In Taiwanese markets, people always use “jin” to express the weight of a product. On average, a whole chicken weighs 4 jins. Enzo wants to get 120 grams of protein by eating chicken. Suppose a whole chicken has 20% protein. How many chickens should he eat at least?

1 jin [math]=[/math] 600 grams

Quarter
Half
One
One and half

29. Question

Franky needs 2 quarts of milk to make some yogurt. If there are 3 cups of milk left in his fridge, how much more milk, in pints, does Franky need?

1quart [math]=[/math] 2 pints

1 pint [math]=[/math] 2 cups

[math]1[/math]
[math]1.5[/math]
[math]2[/math]
[math]2.5[/math]

30. Question

$$51-17x\geq-34$$What is the solution to the inequality?

[math]x\leq5[/math]
[math]x\geq5[/math]
[math]x\leq-5[/math]
[math]x\geq-5[/math]

31. Question

Every Saturday morning at 10:00, Eliza goes to attend Franky’s IBSL math class by bike. Assuming Eliza’s home is 5 kilometers away from Franky s classroom, and Eliza s maximum biking speed is 6 kilometers per hour. How many minutes in advance would Eliza need to leave home to avoid being late?

[math]5[/math]
[math]25[/math]
[math]50[/math]
[math]55[/math]

32. Question

Which of the following numbers satisfies the inequalities [math]2x+3>5[/math] and [math]3x-1\leq4[/math]?

[math]1[/math]
[math]1.5[/math]
[math]2[/math]
[math]2.5[/math]

33. Question

$$3-x\geq4$$$$x\geq a$$If the linear inequalities system above has no solutions where [math]a[/math] is a constant, which of the following values could be [math]a[/math]?

[math]-3[/math]
[math]-2[/math]
[math]1[/math]
[math]0[/math]

34. Question

$$|2x+7|=-13$$Which of the following numbers are the solutions to the equation above?

[math]3,-10[/math]
[math]3[/math]
[math]-10[/math]
No solutions

35. Question

$$|2+x|<5$$Which of the following numbers is not a solution to the inequality above?

[math]3[/math]
[math]2[/math]
[math]0[/math]
[math]-2[/math]

36. Question

Which of the following absolute value inequalities has the solution [math]-3\leq x\leq7[/math]?

[math]|x-2|\leq5[/math]
[math]|x-2|\geq5[/math]
[math]|x+2|\leq5[/math]
[math]|x+2|\geq5[/math]

37. Question

$$|x+2|=|x+3|$$How many solutions does the equation have?

None
One
Two
Three