10 Most Common DAT Quantitative Reasoning Math Questions
Preparing for the DAT Math test? Want a preview of the most common mathematics questions on the DAT Math test? If so, then you are in the right place.
The mathematics section of the DAT can be a challenging area for many test-takers, but with enough patience, it can be easy and even enjoyable!
Preparing for the DAT Math test can be a nerve-wracking experience. Learning more about what you’re going to see when you take the DAT can help to reduce those pre-test jitters. Here’s your chance to review the 10 most common DAT Math questions to help you know what to expect and what to practice most. Try these 10 most common DAT Math questions to hone your mathematical skills and to see if your math skills are up to date on what’s being asked on the exam or if you still need more practice.
Make sure to follow some of the related links at the bottom of this post to get a better idea of what kind of mathematics questions you need to practice.
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Right triangle ABC is shown below. Which of the following is true for all possible values of angles A and B?
tan A = tan B
sin A = cos B
tan\(^2\) A=tan\(^2\) B
tan A=1
Show answer and explanation
B
By definition, the sine of an acute angle is equal to the cosine of its complement.
Since angle A and B are complementary angles, therefore:
\(sin \space A = cos \space B\)
What is the value of y in the following system of equations?
\(3x-4y= -20\)
\(-x+2y= 10\)
\(-1\)
\(-2\)
1
4
5
Show answer and explanation
E
Solve the system of equations by the elimination method.
\(3x-4y= -20\)
\(-x+2y=10\)
Multiply the second equation by 3, then add it to the first equation.
\(3x-4y= -20\)
\(3(-x+2y=10)\)
\(\Downarrow\)
\(3x-4y= -20\)
\(-3x+6y=30)\)
add the equations
\(2y=10⇒y=5\)
How long does a 420–miles trip take moving at 50 miles per hour (mph)?
4 hours
6 hours and 24 minutes
8 hours and 24 minutes
8 hours and 30 minutes
10 hours and 30 minutes
Show answer and explanation
C
Use distance formula:
\(Distance = Rate × time ⇒ 420 = 50 × T\), divide both sides by 50.
\(\frac{420}{50} = T ⇒ T = 8.4 \space\) hours.
Change hours to minutes for the decimal part. 0.4 hours \(= 0.4 × 60 = 24\) minutes.
From the figure, which of the following must be true? (Figure not drawn to scale)
\(y = z\)
\(y = 5x\)
\(y≥x\)
\(y+4x=z\)
\(y>x\)
Show answer and explanation
D
\(x\) and \(z\) are colinear. \(y\) and \(5x\) are colinear. Therefore,
\(x+z=y+5x\),subtract \(x\) from both sides,then,\(z=y+4x\)
When \(40\%\) of 60 is added to \(12\%\) of 600, the resulting number is:
24
72
96
140
180
Show answer and explanation
C
\(40\%\) of 60 equals to:\( 0.40×60=24\)
\(12\%\) of 600 equals to: \(0.12×600=72\)
\(40\%\) of 60 is added to \(12\%\) of 600: \(24+72=96\)
A ladder leans against a wall forming a \(60^\circ\) angle between the ground and the ladder. If the bottom of the ladder is 30 feet away from the wall, how long is the ladder?
30 feet
40 feet
50 feet
60 feet
120 feet
Show answer and explanation
D
The relationship among all sides of the special right triangle
\(30^\circ-60^\circ- 90^\circ\) is provided in this triangle:
In this triangle, the opposite side of \(30^\circ\) angle is half of the hypotenuse.
Draw the shape of this question:
The latter is the hypotenuse. Therefore, the latter is 60 ft.
If \(40 \%\) of a class are girls, and \(25 \%\) of girls play tennis, what percent of the class plays tennis?
\(10 %\)
\(15 %\)
\(20 %\)
\(40 %\)
\(80 %\)
Show answer and explanation
A
The percent of girls playing tennis is: \(40 \% × 25 \% = 0.40 × 0.25 = 0.10 = 10 \%\)
In five successive hours, a car travels 40 km, 45 km, 50 km, 35 km, and 55 km. In the next five hours, it travels with an average speed of 50 km per hour. Find the total distance the car traveled in 10 hours.
425 km
450 km
475 km
500 km
1000 km
Show answer and explanation
C
Add the first 5 numbers. \(40 + 45 + 50 + 35 + 55 = 225\)
To find the distance traveled in the next 5 hours, multiply the average by the number of hours.
\(Distance = Average × Rate = 50 × 5 = 250\)
Add both numbers. \(250 + 225 = 475\)
From last year, the price of gasoline has increased from $1.25 per gallon to $1.75 per gallon. The new price is what percent of the original price?
\(72 \%\)
\(120 \%\)
\(140 \%\)
\(160 \%\)
\(180 \%\)
Show answer and explanation
C
The question is this: 1.75 is what percent of 1.25?
Use the percent formula:
\(part = \frac{percent}{100}× whole \)
\(1.75 = \frac{percent}{100}× 1.25 ⇒ 1.75 = \frac{percent ×1.25}{100}⇒175 = percent ×1.25 ⇒ percent =\frac{175}{1.25}= 140\)
if \(\frac{3x}{16} = \frac{x – 1}{4}\) = ?
\(\frac{1}{4}\)
\(\frac{3}{4}\)
3
4
\(\frac{9}{4}\)
Show answer and explanation
D
Solve for \(x.\frac{3x}{16} = \frac{x – 1}{4}\)
Multiply the second fraction by 4.
\(\frac{3x}{16}=\frac{4(x-1)}{4×4}\)
\(3x=4x-4\)
\(0=x-4\)
\(4=x\)
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