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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
\(\frac{2^{x1}}{2^{1x}}\) is equal to which of the following? A. \(4^{x1}\) B. \(4^{1x}\) C. \(4^{2x}\) D. \(4^{2x}\) E. \(4^x\) ==> You get \(\frac{2^{x1}}{2^{1x}} =2^{x1(1x)}=2^{2(x1)}=4^{x1}\). The answer is A. Answer: A
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07 Apr 2017, 02:02
It’s well known that a company's profit=10,000x50x^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 numberthe first number)/2 +1=range/2+1, so from range/2+1=25, range/2=251=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 n3. 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
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If the distances between two consecutive points are the same, what is the value of A in terms of x and y? A. 3y2x B. 3x2y C. 2x3y D. 2y3x E. 3y+2x ==> The distance between 2 consecutive points=d, hence d=yx and A=y+2d=y+2(yx)=3y2x. 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 \(a>b>0\), \(a^2+b^2=6ab\), \(\frac{(a+b)}{(ab)}=\)? 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 \((ab)^2=a^2+b^22ab=6ab2ab=4ab\), you get \(ab=\sqrt{4ab}\) and \(\frac{(a+b)}{(ab)}=\sqrt{8ab}/\sqrt{4ab}=2\). Therefore, the answer is B. Answer: B
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20 Apr 2017, 01:43
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From the above, you get \(h:(sr)/2=√3:1\) and \(h=√3(sr)/2\). The answer is A. Answer: A
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21 Apr 2017, 01:29
10.000001=? 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 \(a^2b^2=(a+b)(ab)\), and thus \(10.000001=1^20.001^2=(1+0.001)(10.001)=1.001*0.999\). 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, (ab)/(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 (ab)/(a+b)=(65)/(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=2x5 B. y=6x5 C. y=(x/2)5 D. y=(x/3)5 E. y=(2x5)/3 ==> According to the ivy approach, is:”=”, greater than:”+”, hence you get 2x=5+3y. Thus, from 3y=52x, y=(2x5)/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 \(a^2b^2=(ab)(a+b)\), 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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