Practice ECAT Mathematics questions with answers and explanations.
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Let the son's age be x and father's age 3x.
Then 3x + 10 = 2(x + 10), giving x = 10.
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Let tens digit be a and units digit b; then a + b = 11 and 9(b - a) = 27.
So b - a = 3, giving a = 4 and b = 7.
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Substitute x = -4 into the expression.
Then y = 3(-4) - 2 = -14.
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Slope-intercept form is y = mx + c.
With m = 2 and c = 3, the equation is y = 2x + 3.
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A point with x = 0 gives the y-intercept 4.
Using y = mx + c with m = -1 gives y = -x + 4.
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The sum of the roots is 6.
Their average is 6/2 = 3.
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For two positive integers a and b, gcd(a,b) × lcm(a,b) = ab.
This identity links common factors and common multiples.
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At 3:00, the minute hand points at 12 and the hour hand at 3.
Three hour intervals correspond to 3 × 30° = 90°.
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If n ≡ 4 mod 7, then 2n ≡ 8 mod 7.
The remainder of 8 divided by 7 is 1.
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At 6:00, the hands point in opposite directions.
Opposite rays form a straight angle of 180°.
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Add 5 to both sides to get 3x > 15.
Dividing by 3 gives x > 5.
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Adding the equations gives twice the larger number: 50 + 14 = 64.
Dividing by 2 gives 32.
