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Shuhang L.

Columbia University Graduate Student

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SAT

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Question:

Line l contains the points (3,1) and (4,4). If line m is a different line, parallel to line l in the same coordinate plane, which of the following could be the equation of line m? A. y = 3x + 6 B. y = 1/3x - 3 C. y = -3x - 8 D. y = -8x + 3

Shuhang L.

Answer:

As in line 1, we know that y =ax+b, line 1 goes through points (3,1) and (4,4) So 1 =3a+b(equation 1), and 4 = 4a+b (equation 2). let equation 2 - equation 1, we get 3 = a Plug a back into equation 1, 1 =9+b so that b = -8. So, equation for line 1 is y =3x-8 line 2, y =cx+d is parallel to line 1, so c=3. In the answer, only answer A has the parameter c =3. So the answer for this problem is A.

Pre-Calculus

TutorMe

Question:

Let the function h be defined by h(x) = 2 cos(10x) + 12. The maximum value of h is attained at which of the following values of x?

Shuhang L.

Answer:

cos(0+2*a*pi) =1, cos(pi/2+ b*pi) = 0, cos(pi+2*c*pi)=-1, a,b,c are integers, -1<cos(x)<1, when 10x = 2*a*pi, h is attained at its maximum. So, x =(a*pi)/5

GRE

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Question:

If the group of students eats 2 cookies, 3 sandwiches and drinks 2 cokes, the bill amounts to $74. If the group of students eats 5 cookies, 6 sandwiches and drinks 4 coke, the bill amounts to $128. If the group of students eats 3 cookies, 3 sandwiches and drinks 2 coke, then what should the group pay?

Shuhang L.

Answer:

set price per cookie = x, price per sandwich = y, price per coke = z, we have 2x+3y+2z = 74 as equation 1 5x+ 6y+4z = 128 as equation 2 we want 3x+3y+2z equation2 - equation1 = 3x+3y+2z so the result should be 128-74 which is $54

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