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05 Apr 2017, 01:22
If (4/9)÷n=3/5, n=?

A. 20/27

B. 27/20

C. 10/9

D. 9/10

E. 9/4

==>(4/9)÷n=3/5 -> (4/9)(1/n)=3/5. And 4/9n=3/5 -> n=(4/9)(5/3)=20/27.

Hence, the answer is A.

Answer: A

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06 Apr 2017, 01:02
\(\frac{2^{x-1}}{2^{1-x}}\) is equal to which of the following?

A. \(4^{x-1}\)

B. \(4^{1-x}\)

C. \(4^{2x}\)

D. \(4^{-2x}\)

E. \(4^x\)

==> You get \(\frac{2^{x-1}}{2^{1-x}} =2^{x-1-(1-x)}=2^{2(x-1)}=4^{x-1}\).

The answer is A.

Answer: A

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07 Apr 2017, 02:02
It’s well known that a company's profit=10,000x-50x^2, where x is the number of workers. If the profit of the company is the greatest, what is the value of x?

A. 5

B. 10

C. 50

D. 80

E. 100

==> From \(y=f(x)=ax^2+bx+c\), if \(x=\frac{-b}{2a}\), f(x) becomes either maximum or minimum. Thus, profit=\(-50x^2+10,000x\), and in order for the profit to become the greatest, you get \(x=\frac{-10,000}{2(-50)}=100\).

The answer is E.

Answer: E

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09 Apr 2017, 18:37
What is the range of 25 consecutive even numbers?

A. 44

B. 46

C. 48

D. 50

E. 52

==> The number of consecutive even numbers=(The last number-the first number)/2 +1=range/2+1, so from range/2+1=25, range/2=25-1=24, you get range=2(24)=48.

Therefore, the answer is C.

Answer: C

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09 Apr 2017, 18:38
If 1 male, 2 females, and 1 child are to be selected at random from 8 males, 10 females, and 8 children, respectively, how many such cases are possible?

A. 980

B. 1,440

C. 1,880

D. 2,480

E. 2,880

==> From (8C1)(10C2)(8C1)=(8)(10*9/2!)(8)=2,880, the answer is E.

Answer: E

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12 Apr 2017, 01:14
When \(5^{11}\) and \(2^n7^2\) have the same number of factors, what is the value of n?

A. 2

B. 3

C. 4

D. 5

E. 6

==> From 11+1=(n+1)(2+1), you get 12=3(n+1), and n-3.

Therefore, the answer is B.

Answer: B

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13 Apr 2017, 18:16
If \(x^{-2}+x^{-1}=0\), \(x=\)?

A. -1

B. 0

C. 1

D. 0, 1

E. -1, 0

==> If you multiply x^2 on both sides, you get 1+x=0, x=-1.

The answer is A.

Answer: A

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14 Apr 2017, 07:37
Attachment:

a.png [ 1.09 KiB | Viewed 242 times ]
If the distances between two consecutive points are the same, what is the value of A in terms of x and y?

A. 3y-2x

B. 3x-2y

C. 2x-3y

D. 2y-3x

E. 3y+2x

==> The distance between 2 consecutive points=d, hence d=y-x and A=y+2d=y+2(y-x)=3y-2x.

The answer is A.

Answer: A

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16 Apr 2017, 18:29
If 3 juniors from 8 juniors are selected at random to make a committee, how many cases are possible?

A. 8

B. 28

C. 35

D. 42

E. 56

==> In general, you solve probability questions using nCr, a combination. In other words, from 8C3=56, the answer is E.

Answer: E

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16 Apr 2017, 18:30
If xy>0, which of the following must be positive?

A. \(x\)

B. \(y\)

C. \(x^2y\)

D. \(y^2x\)

E. \(x^3y\)

==> Squares are always positive, so the inequality sign doesn’t change even if you multiply or divide. Thus, from xy>0 and \((x^2)xy>(x^2)0\), you get \(x^3y>0\).

The answer is E.

Answer: E

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19 Apr 2017, 01:37
If \(a>b>0\), \(a^2+b^2=6ab\), \(\frac{(a+b)}{(a-b)}=\)?

A. 1

B. \(\sqrt{2}\)

C. \(\sqrt{3}\)

D. \(\sqrt{5}\)

E. 2

==> From \((a+b)^2=a^2+b^2+2ab=6ab+2ab=8ab\), you get \(a+b=\sqrt{8ab}\)

And from \((a-b)^2=a^2+b^2-2ab=6ab-2ab=4ab\), you get \(a-b=\sqrt{4ab}\) and

\(\frac{(a+b)}{(a-b)}=\sqrt{8ab}/\sqrt{4ab}=2\).

Therefore, the answer is B.

Answer: B

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20 Apr 2017, 01:43
Attachment:

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Attachment:

b.png [ 2.23 KiB | Viewed 211 times ]
From the above, you get \(h:(s-r)/2=√3:1\) and \(h=√3(s-r)/2\). The answer is A.

Answer: A

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21 Apr 2017, 01:29
1-0.000001=?

A. 1.001*0.999

B. 1.0001*0.9999

C. 1.001*0.9999

D. 1.0001*0.999

E. 1.01*0.99

==> You get \(a^2-b^2=(a+b)(a-b)\), and thus \(1-0.000001=1^2-0.001^2=(1+0.001)(1-0.001)=1.001*0.999\).

The answer is A.

Answer: A

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24 Apr 2017, 02:49
When a certain coin is flipped, the probability that the coin will land on head or tail is 1/2 each. If the coin is flipped 4 times, what is the probability that it will land on tail at least twice on 4 flips?

A. \(\frac{3}{8}\)

B. \(\frac{1}{16}\)

C. \(\frac{1}{2}\)

D. \(\frac{5}{8}\)

E. \(\frac{11}{16}\)

==> In general, you solve probability questions using nCr combination. In other words, from TTHH, there are (4!/2!/2!)=6 possibilities, so you get (1/2)(1/2)(1/2)(1/2)*6=3/8. From TTTH, there are (4!/3!)=4 possibilities, so you get (1/2)(1/2)(1/2)(1/2)*4=1/4. From TTTT, there is only 1 possibility, so you get (1/2)(1/2)(1/2)(1/2)=1/16 and (3/8)+(1/4)+(1/16)=(6+4+1)/16=11/16.

The answer is E.

Answer: E

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24 Apr 2017, 02:50
Which of the following is equal to \(\frac{(n+2)!}{n!}\)?

A. \(n(n+1)\)

B. \(1+(\frac{2}{n})\)

C. \(n^2+3n+2\)

D. \(n^2+2n\)

E. \(n+2\)

==> Since (n+2)!=(n+2)(n+1)n!, from (n+2)!/n!=(n+2)(n+1)n!/n!=(n+2)(n+1)

=\(n^2+3n+2\), the answer is C.

Answer: C

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26 Apr 2017, 01:17
When a/b=1.2, (a-b)/(a+b)=?

A. \(\frac{1}{15}\)

B. \(\frac{1}{11}\)

C. \(\frac{1}{9}\)

D. \(\frac{3}{8}\)

E. \(\frac{1}{3}\)

==> From a/b=1.2=6/5, if you substitute a=6 and b=5, you get (a-b)/(a+b)=(6-5)/(6+5)=1/11.

Therefore, the answer is B.

Answer: B

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27 Apr 2017, 01:51
If two times x is 5 greater than three times y, what is the value of y, in terms of x?

A. y=2x-5

B. y=6x-5

C. y=(x/2)-5

D. y=(x/3)-5

E. y=(2x-5)/3

==> According to the ivy approach, is:”=”, greater than:”+”, hence you get 2x=5+3y. Thus, from 3y=5-2x, y=(2x-5)/3, the answer is E.

Answer: E

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28 Apr 2017, 01:35
If the sum of the annual salary of n persons is $x and the monthly salary per person is $y, what is the value of n in terms of x and y?

A. \($\frac{x}{12y}\)

B. \($\frac{12x}{y}\)

C. \($12xy\)

D. \($\frac{12y}{x}\)

E. \($\frac{xy}{12}\)

==> If the annual salary per person: s, you get ns=x, s=12y. If you substitue this, you get n(12y)=x, \(n=\frac{x}{12y}\).

Therefore, the answer is A.

Answer: A

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30 Apr 2017, 18:12
\((5+\frac{1}{5})^2-(5-\frac{1}{5})^2\)=?

A. 2

B. 3

C. 4

D. 5

E. 9

==> Since \(a^2-b^2=(a-b)(a+b)\), you get \((5+\frac{1}{5})^2-(5-\frac{1}{5})^2=[(5+\frac{1}{5})-(5-\frac{1}{5})][(5+\frac{1}{5})+(5-\frac{1}{5})]=(\frac{2}{5})(10)=4\).

The answer is C.

Answer: C

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30 Apr 2017, 18:13
If n is the product of 3 consecutive integers, which of the following must be true?

I. a multiple of 2 II. a multiple of 3 III. a multiple of 4

A. I only

B. II only

C. III only

D. I and II only

E. II and III only

==> From n=m(m+1)(m+2) , where m=integer, the product of 3 consecutive integers is always a multiple of 6. Thus, I and II is always true. For III, if m=1, from n=(1)(2)(3)=6, it is not a multiple of 4, hence it is false.

Therefore, the answer is D.

Answer: D

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