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03 Mar 2017, 01:13
If \(x^2=2x+1, x^3\)=？ A. 4x B. 5x+2 C. 5x1 D. 3x+2 E. 3x2 ==> \(x^3=x(x^2)=x(2x+1)=2x^2+x=2(2x+1)+x=5x+2\) Answer: B
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Math Revolution Approach (PS) [#permalink]
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03 Mar 2017, 04:19
MathRevolution wrote: If \(x^2=2x+1, x^3\)=？
A. 4x B. 5x+2 C. 5x1 D. 3x+2 E. 3x2
==> \(x^3=x(x^2)=x(2x+1)=2x^2+x=2(2x+1)+x=5x+2\)
Answer: B How did you get this part? 2x2+x=2(2x+1)+x



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07 Mar 2017, 04:39
chandanindira wrote: MathRevolution wrote: If \(x^2=2x+1, x^3\)=？
A. 4x B. 5x+2 C. 5x1 D. 3x+2 E. 3x2
==> \(x^3=x(x^2)=x(2x+1)=2x^2+x=2(2x+1)+x=5x+2\)
Answer: B How did you get this part? 2x2+x=2(2x+1)+x Since x^2 = 2x+1 (given) So, 2 . x^2 = 2 . (2x+1) chandanindira



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08 Mar 2017, 01:16
\(Let A=6^2^0, B=2^6^0, and C=4^5^0.\) Which of the following is true? A. A<B<C B. A<C<B C. B<A<C D. B<C<A E. C<B<A ==> You can compare the big and small numbers by making the base or the exponent the same. From\(A=6^2^0, B=2^6^0=(2^3)^2^0=8^2^0\), you get 6<8, which becomes A<B, and from \(B=2^6^0=(2^2)^3^0=4^3^0, C=4^5^0,\) you get 30<50, which becomes B<C. Thus, you get A<B<C. The answer is A. Answer: A
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09 Mar 2017, 02:41
Which of the following is equal to \(3^m7^{m1}\)? \(A. 3(21^m)\) \(B. 7(21^m)\) \(C. 3(21^{m1})\) \(D. 7(21^{m1})\) \(E. 21^{m1}\) ==> From \(3^m7^m^^1=3(3^m^^1)(7^m^^1)=3(3*7)^m^^1=3(21^m^^1)\), the answer is C. Answer: C
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10 Mar 2017, 03:13
\(\frac{5.09}{0.149}\) is closest to which of the following? A. 0.34 B. 3.4 C. 34 D. 340 E. 3,400 From \(\frac{5.09}{0.149} = \frac{5.10}{0.15} = \frac{510}{15} =34\), the answer is C. Answer: C
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12 Mar 2017, 18:47
In the xy plane, what is the slope between yintercept and a negative xintercept of \(y=x^2+x6\)? A. 2 B. 3 C. 2 D. 4 E. 6 ==> From y=x2+x6=(x+3)(x2)=0, the xintercept becomes (3,0) or (2,0), and (0,6). From these, the negative xintercept is (3,0) and the negative yintercept is (0,6). The slope of the straight line that passes through the two points becomes \(\frac{0(6)}{30=2}\) The answer is A. Answer: A
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Updated on: 16 Mar 2017, 18:21
If m and n are positive integers, what is the number of factors of \(3^m7^n\)? A. mn+m+n B. mn+1 C. (m1)(n1) D. (m+1)(n+1) E. mn ==> The number of factors of \(3^m7^n\) becomes (m+1)(n+1). The answer is D. Answer:D
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15 Mar 2017, 02:13
Of the people who purchase a house, 60% considers the landscape and 80% considers the color of the house. If 10% of the people who purchase a house considers neither the landscape nor the color of the house, what percent is the people who consider both the landscape and the color of the house? A. 40% B. 45% C. 50% D. 55% E. 60% Attachment:
question.png [ 4.97 KiB  Viewed 394 times ]
If you set the intersection as a%, you get the figure above. Then, from (60a)+a+(80a)=90, you get 140a=90 and a=50. Therefore, the answer is C. Answer: C
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16 Mar 2017, 01:27
If \(3^x=\frac{1}{27}\), then x=? A. 3 B. 2 C. 1 D. 2 E. 3 ==>From \(3^x=\frac{1}{27}=3^^3\) you get x=3. The answer is A. Answer: A
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19 Mar 2017, 18:02
Which of the following is equal to (x+2)!/(x+1)!? A. x1 B. 1+(1/x) C. 1 D. x+1 E. x+2 ==> According to n!=n(n1)!, you get (x+2)!/(x+1)!=(x+2)(x+1)!/(x+1)!=x+2. Therefore, the answer is E. Answer: E
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19 Mar 2017, 18:07
Attachment:
1.png [ 6.76 KiB  Viewed 389 times ]
If DB=2, AC=12, and X is the center of the circle shown as the above figure, what is the area of the circle? A. \(20π\) B. \(80π\) C. \(100π\) D. \(120π\) E. \(160π\) Attachment:
23.png [ 5.03 KiB  Viewed 389 times ]
You get the figure shown above, and according to the Pythagorean Theorem, you get \(r^2=(r2)^2+6^2=r^24r+4+36\), and if you get rid of \(r^2\) on both sides and simplify the equation, from 4r=40, you get r=10. Thus, it becomes the area of the circle, which is \(π10^2=100π\). The answer is C. Answer: C
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20 Mar 2017, 03:42
How many possible 6digit code numbers can be formed from three a, two b, and one c? A. 40 B. 50 C. 60 D. 70 E. 80 ==> You get a,b,b, c,c,c, which is 6!/(2!)(3!)=60. Therefore, the answer is C. Answer: C
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22 Mar 2017, 02:49
If the average (arithmetic mean) of 5 consecutive multiples of 5 is 30, what is the smallest number of them? A. 5 B. 10 C. 15 D. 20 E. 25 ==> If the average of 5 consecutive multiples of 5 is 30, from 20,25,30,35,40, the smallest multiple of 5 becomes 20. Therefore, the answer is D. Answer: D
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23 Mar 2017, 01:22
What is the number of integers x such that \(4<x^24x+4<16\)? A. 1 B. 2 C. 3 D. 4 E. 5 ==> Since \(x^24x+4=(x2)^2\), from \(4<(x2)^2<16\), you get 4<x2<2 or 2<x2<4, and if you simplify it, from 2<x<0 or 4<x<6, you get x=integer=1,5, and thus 2. Therefore, the answer is B. Answer: B
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24 Mar 2017, 03:56
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 E. II and III ==> If n is the product of 3 consecutive integers, it is always even and has 3, so it is always a multiple of 6. Thus, I and II is correct and for III, since n=1*2*3=6 is not a multiple of 4, hence it is incorrect. The answer is D. Answer: D
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26 Mar 2017, 18:32
If Tom goes y miles in x hours, how many miles does he go per minute, in terms of x and y? A. 60x/y B. y/60x C. 60y/x D. x/60y E. 60xy ==>You get miles:hours=y(miles):x(hours)=y(miles):60x(minutes), and from y:60x=some:1, you get some=y/60x. The answer is B. Answer: B
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29 Mar 2017, 02:01
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, you get is:”=” and greater than:”+”, so you get 2x=5+3y. From 3y=2x5, y=(2x5)/3, the answer is E. Answer: E
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30 Mar 2017, 02:19
If the sum of the annual salaries 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. $x/12y B. $12x/y C. $12xy D. $12y/x E. $xy/12 ==> Since the monthly salary per person is $y, the annual salary per person becomes $12y and the total sum of the annual salaries of n number of people becomes $12ny. Since it is $x, from $12ny=$x, you get n=x/12y. The answer is A. Answer: B
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31 Mar 2017, 01:35
√3 is what percent of √12? A. 20% B. 25% C. 30% D. 46% E. 50% ==> According to the ivy approach, you get is:”=”, what: “some”, and percent:”1/100”. Also, you substitute √12=2√3, and from √3=some(1/100)2√3, if you get rid of √3 on both sides, you get 1=(some)2/100, some=50. The answer is E. Answer: E
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