Excellent QR Questions

[DrGeek]

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#1)
....(a - b)(c - d).....-5...........(a - c)(b - d)
if _____________ = ___, find _____________
....(b - c)(d - a)......3...........(a - b)(c - d)

#2)
assume ad = bc and h^2 = c/a = d/b
Is Ax^3 + bx^2 + cx + d divisible by x^2 + h^2

A. Divisible
B. Indivisible
C. Can't determine

#3)
The seating capacity of an auditorium is 600. For a certain performance, with the auditorium not filled to capacity, the receipts were $330. Admission prices were 75 cents for adults and 25 cents for children. If a represents the number of adults at the performance, find the minimum value of a satisfying the given conditions.

 

[R.L.H]

#1)
....(a - b)(c - d).....-5...........(a - c)(b - d)
if _____________ = ___, find _____________
....(b - c)(d - a)......3...........(a - b)(c - d)

#2)
assume ad = bc and h^2 = c/a = d/b
Is Ax^3 + bx^2 + cx + d divisible by x^2 + h^2

A. Divisible
B. Indivisible
C. Can't determine

#3)
The seating capacity of an auditorium is 600. For a certain performance, with the auditorium not filled to capacity, the receipts were $330. Admission prices were 75 cents for adults and 25 cents for children. If a represents the number of adults at the performance, find the minimum value of a satisfying the given conditions.

Is answer for #3 360 adults?

 

[DrGeek]

Is answer for #3 360 adults?

close but not right. The minimum value that satisfies the given conditions is greater than 360 (i.e. a > 360). So answer is 361

 

[luder98]

1. Mistyped?
2. A. I doubt that they expect you to be able to solve this on the DAT.
3. Yes, 361. The key word is "not filled".

 

[RozhonDDS]

can someone show the work for question #3?

 

[R.L.H]

close but not right. The minimum value that satisfies the given conditions is greater than 360 (i.e. a > 360). So answer is 361

right, it is 361.

 

[luder98]

can someone show the work for question #3?

0.75a + 0.25c = 330 --> c = (330-0.75a)/0.25
a + c < 600 (not filled)
a + (330-0.75a)/0.25 < 600
0.25a + 330 -0.75a < 600*0.25 = 6*25 = 150
330 - 0.5a < 150
0.5a > 330 - 150 = 180
(1/2)a > 180
a > 180*2 = 360
Since a is an integer, the first one that is greater than 360 is 361.

 

[DrGeek]

1. Mistyped?

NO
Here is the solution for #1:

....(a - b)(c - d).....-5
..._____________ = ___
....(b - c)(d - a)......3
************************
....(b - c)(d - a).....-3
..._____________ = ___
....(a - b)(c - d)......5
************************
........(b - c)(d - a)............-3
...1 - _____________ = 1 - ___
........(a - b)(c - d).............5
************************
........ac - bc - ad + bd - bd + ab + cd - ac............-3
.......________________________________ = 1 - ______
........(a - b)(c - d)..............................................5
************************
.....(a - c)(b - d).............3........8
... _____________ = 1 + ____ = ____
.....(a - b)(c - d).............5........5