The figure below shows two triangle with angles as labeled. What is the measure of angle E in terms of angles u and v?
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TJ Prep Problems
TJ Prep practice problems for our students and readers. The problems provide a very small sampling of what Optimal TJ Prep students work with.
An Area Problem for TJ Prep/Blair Prep/HSPT/SSAT Prep. (Medium). Target Time. 10-35 seconds.
The figure below shows a square with side 8 and four semicircles (with diameter equal to 1/2 the side of the square) as shown. What is the area of the region striped with yellow lines?
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A Word Problem for TJHSST/HSPT/Blair Test Prep(Medium). Target Time. 15-230 seconds.
The area of a circular photograph with diameter 8" must be reduced by what percent so that it exactly fit in a circular digital photo frame of radius 2.5 ?
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A Word Problem for TJHSST Admissions/HSPT/SSAT Prep. (Easy). Target Time. 15-25 seconds.
Joe and Ram are playing a ball exchange game. At the outset, Joe has 300 more balls than Ram. After Joe gives 100 balls to Ram, Joe has 1.5 times as many balls as Ram. How many balls did each have to start with?
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A Geometry Problem for TJHSST Admissions/SHSAT/HSPT Prep. (Hard). Target Time. 20-40 seconds.
The figure below shows a squareABCD, a trapezoid BCDF and a triangle DEF. What is the ratio of the area of the trapezoid to the area of the triangle.
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An Algebra Problem for TJ Exam/HSPT/SSAT Prep. (Medium). Target Time. 10-35 seconds.
Simplify the expression (2 X - 3) (3 + 2 X) + 9.
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An Arithmetic Problem for TJHSST Admissions Exam/HSPT/SSAT Prep (Medium). Target Time. 15-35 seconds.
If the total value of online sales on Black Friday sales in 2016 decrease by 10% and the total value of Cyber Monday sales increase by 15%, the ratio of Cyber Monday sales to Black Friday sales in 2016 will be how many times the ratio in 2015?
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A Geometry Problem for TJ Exam Prep. (Easy). Target Time. 15-30 seconds.
The figure below shows a triangle with angles as marked. What is a + b ?
A Geometry Problem for TJ Admissions Test/Montgomery Blair/HSPT Prep. (Medium). Target Time. 20-35 seconds.
The figure below, not drawn to scale, shows a rectangle ABCD and a triangle CDE with altitude EF. If the ratio of area of triangle CDE to the area of the rectangle ABCD is 5:3, what is the ratio of EF:BC?
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An Algebra Problem for TJ Admissions Exam/HSPT/Montgomery Blair Admissions Prep. (Medium). Target Time. 20-35 seconds.
if a = X^2 + 1 and b = X^2 - 1, what is X in terms of a and b?
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An Algebra Problem for TJ Admission Test/HSPT/SSAT Prep. (Medium).
If a, b, P, Q and T are nonzero integers and a/b = P/Q and P/T = (3a)/(2b), what is the value of T?
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An Algebra Problem for TJHSST Admission Test/HSPT/SSAT. (Easy). Target Time. 15-35 seconds.
X and Y are integers (<16) such that X^3 = Y^2. What is the greatest possible difference between X-Y ?
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A Percent Problem for TJHSST Admission Test. (Medium). Target Time. 15 to 55 seconds.
A is 20% greater than B. What is B when A is 200 ?
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A Arithmetic Word Problem for TJ Exam Prep/HSPT/SSAT Prep. (Easy). Target Time. 15-35 seconds.
If 18 frogs catch 300 insects in 6 Hrs then working at the same rate, 12 frogs will take how many hours to catch 1800 insects ?
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An Arithmetic Problem for TJ Admissions Prep/HSPT. (Medium). Target Time. 30-45 seconds.
The sum of three different positive integers is 15. What is difference between the highest and the lowest possible products of any three such numbers ?
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An arithmetic Problem for TJ Exam Prep. (Medium). Target Time. 25-35 seconds.
A employee was asked to reduce the price of a popular phone by 20%. She erroneously increased the price by 20%. The "incorrect" price should be reduced by what % to achieve the desired result ?
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A n Algebra Proportion for TJ Admission test/HSPT/SSAT Prep. (Medium). Target Time. 15-35 seconds.
If mangoes cost of $3N for 6 lbs, what is the price of M lbs of mangoes ?
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A Ratio Problem for TJ Exam Prep/SHSAT/HSPT/SSAT Prep (Medium). arget Time. 15-30 seconds.
If M and P are non zero integers, and 4 M = 5 P, how many P's = 8 (M + P) ?
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A Function Problem for SAT Math Level II Subject Test (Medium). Target Time. 15-30 seconds.
The figure below shows two functions f(x) and g (X). For how many values of x (shown in the figure, f (X) + g (X) = f (X) - g (X) ?
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A Geometry Problem for TJ Admissions Test Prep. (Medium). Target Time. 20-40 seconds.
The figure below shows a quadrilateral with both diagonals as shown. and angles as marked.
1. What is the sum of a, b, c, d in terms of p and q ?
2. If p > q, which is greater a + b or c + d ?
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