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Math Revolution GMAT Instructor
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Re: Math Revolution Approach (DS)
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18 Aug 2017, 01:50
Is the total profit from the sales of 3 products greater than $6? 1) The least profit from the sales of the 3 products is at least $2.1 2) The 2nd largest profit from the sales of the 3 products is at least $3.1. => Condition 1) Since the minimum profit of 3 products is $2.1, the total profit of them is greater than or equal to $2.1 x 3 = $6.3, which is greater than $6. Thus this is sufficient. Condition 2) Since the 3nd largest profit is at least $3.1, the sum of the first and the second products is at least $6.2, which is greater than $6. Thus this is sufficient too. Ans: D
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Re: Math Revolution Approach (DS)
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20 Aug 2017, 19:08
If xy≠0, is x>y？ 1) x=2y 2) x=y^4 =>Condition 1) x = 2y = 2y > y. Thus this is sufficient. Condition 2) If y = 2, then x = 16 and so x > y. If y = ½, then x = 1/16 and so x < y. This is not sufficient. Ans: A
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Re: Math Revolution Approach (DS)
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20 Aug 2017, 19:09
Is a positive integer x an odd number? 1) The smallest prime factor of x is 7. 2) The greatest prime factor of x is 7. =>Condition 1) 2 cannot be a factor of x, since the smallest prime factor of x is 7. Condition 2) Consider n = 2 and n =3. Ans: A
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Re: Math Revolution Approach (DS)
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23 Aug 2017, 01:20
What is the value of a positive integer k? 1) When k is divided by 5, the remainder is 3. 2) When k is divided by 3, the remainder is 2. =>Condition 1) & 2) k = 8, 23, … Both conditions together are not sufficient either. Ans: E
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Re: Math Revolution Approach (DS)
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24 Aug 2017, 01:28
If x, y, and z are positive integers, is x+y divisible by 5? 1) x+z is divisible by 5 2) y+z is divisible by 5 => Consider 1) & 2) x = 1, y = 1, z = 4 : x + y is not divisible by 5 x = 5, y = 5, z = 0 : x + y is divisible by 5 Ans: E
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Math Revolution GMAT Instructor
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Re: Math Revolution Approach (DS)
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25 Aug 2017, 01:10
We define “A mod n” as the remainder when A is divided by n. What is the value of “A mod 6”? 1) A mod 4 = A mod 12 2) A mod 3 = 2 => Condition 1) A = 0, 1, 2, 3. This is not sufficient. Condition 2) A = 2, 5. This is not sufficient. Condition 1) & 2) From the condition 2), we have four cases as follows. A = 12k + 2 A = 12k + 5 A = 12k + 8 A = 12k + 11 From the condition 1), A should be the case that A = 12k + 2 = 6*(2k) + 2. Thus both conditions together are sufficient. Ans: C
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Re: Math Revolution Approach (DS)
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27 Aug 2017, 19:08
What is the median of 12, y, and x? 1) x+y=24 2) y=6 => Condition 1) If x = y = 12, then the median of them is 12. If x < y, then the median of them 12, since x < 12 < y. If x > y, then the median of them 12, since y < 12 < x. This is sufficient. Condition 2) Since we don’t know x, we don’t identify their median. This is not sufficient. Ans: A
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Re: Math Revolution Approach (DS)
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27 Aug 2017, 19:10
If x^3y^4z^5<0, is xyz>0? 1) y<0 2) x<0 =>The original condition x^3y^4z^5<0 is equivalent to xy < 0 after dividing both sides of the inequality by x^2y^4z^4. Then the question is equivalent to y>0, since xy < 0 from the equivalent condition. Thus the condition 1) is sufficient, since the question is if y > 0. Ans: A
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Re: Math Revolution Approach (DS)
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30 Aug 2017, 01:25
The probability that event A occurs is 0.5 and the probability that event B occurs is 0.7. What is the probability that event A occurs but not event B? 1) Event A and event B are independent. 2) The probability that neither event A nor event B occurs is 0.15. =>Condition 1) We call an event A and an event B independent if P(A∩B) = P(A)*P(B). P(A∩B) = P(A)*P(B) = 0.5 * 0.7 = 0.35. P(A∩BC) = P(A)  P(A∩B) = 0.5 – 0.35 = 0.15. This is sufficient. Condition 2) 1 – P(A∪B) = 0.15. It means P(A∪B) = 0.85. P(A∪B) = P(A) + P(B)  P(A∩B) = 0.5 + 0.7  P(A∩B) = 0.85. Thus P(A∩B) = 0.15. P(A∩B^C) = P(A)  P(A∩B) = 0.5 – 0.35 = 0.15. This is also sufficient too. Ans: D
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Re: Math Revolution Approach (DS)
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31 Aug 2017, 01:23
If x+5=y+5, what is the value of x+y? 1) xy<0 2) x>3 and y<3 =>Condition 1) x+5=y+5 is equivalent to (x+5)^2=(y+5)^2 or (x+5)^2(y+5)^2 = 0. (x+5)^2(y+5)^2 = (x+y+10)(xy) = 0. Then x = y or x + y + 10 = 0. Since x cannot be equal to y, x + y = 10. This is sufficient. Condition 2) x+5=y+5 is equivalent to (x+5)^2=(y+5)^2 or (x+5)^2(y+5)^2 = 0. (x+5)^2(y+5)^2 = (x+y+10)(xy) = 0. Then x = y or x + y + 10 = 0. Since x > 3 and y < 3, x is not equal to y. Thus x + y = 10. This is sufficient. Ans: D
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Re: Math Revolution Approach (DS)
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01 Sep 2017, 03:18
If x+3=y+3, what is the value of x+y? 1) xy<0 2) x>3 and y<3 => 1) xy < 0 We can assume x > 0 and y < 0 without loss of generality. Then we have x + 3 = y  3 x + y = 6 This is sufficient. 2) x > 3 and y < 3 Then we have x + 3 = y  3 x + y = 6 This is sufficient. Ans: D
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Re: Math Revolution Approach (DS)
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03 Sep 2017, 18:41
△ is one operation of addition, subtraction, multiplication, or division. Is 1△3=3△1？ 1) 1△1=1 2) 2△3=6 => 1) 1△1=1 △ could be the multiplication or the division. If △ is the multiplication, 1△3 = 3△1. If △ is the division, 1△3 is not equal to 3△1. This is not sufficient. 1) 2△3=6 △ should be the multiplication only. Then we have 1△3 = 3△1. This is sufficient. Ans: B
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Re: Math Revolution Approach (DS)
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03 Sep 2017, 18:42
Is a positive integer x an odd number? 1) The smallest prime factor of x is 7. 2) The greatest prime factor of x is 7. => 1) Since the smallest prime factor of x is 7, it can’t have a prime factor 2. Thus it should be odd. This is sufficient. 2) Since the greatest prime factor of x is 7, it may have 2 as a prime factor or it may not. Thus it may be odd or may be odd. This is not sufficient. Ans: A
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Re: Math Revolution Approach (DS)
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06 Sep 2017, 01:29
[GMAT math practice question] Is a positive integer x divisible by 12 ? 1) x is divisible by 8 2) x is divisible by 6 =>1) Since 8 is not a multiple of 12, this is not sufficient. 2) Since 6 is not a multiple of 12, this is not sufficient. 1) & 2) Since lcm(8,6) = 24 is a multiple of 12, these are sufficient. Ans: C
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Re: Math Revolution Approach (DS)
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07 Sep 2017, 01:46
[GMAT math practice question] Is x^2+x>0? 1) 0<x<1 2) x^3x<0 => Q: x^2+x>0 ⬄ x(x+1) > 0 ⬄ x < 1 or x > 0 1) 0<x<1 Since the range of the question includes the rage of the condition 1), it is sufficient. 2) x^3x<0 ⬄ x(x^21) < 0 ⬄ x(x+1)(x1) < 0 ⬄ x < 1 or 0 < x < 1 Since the range of the question includes the rage of the condition 2), it is sufficient too. Ans: D
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Re: Math Revolution Approach (DS)
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08 Sep 2017, 01:00
[GMAT math practice question] What is the value of x in 10, 13, 15, 17, and x? 1) The median of them is 15 2) The range of them is 7 => 1) & 2) x = 16, x = 17 We have two solutions. The answer is not unique. This is not sufficient. Thus the answer is E. Ans: E
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Re: Math Revolution Approach (DS)
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10 Sep 2017, 18:21
[GMAT math practice question] xy=? 1) x and y are integers 2) xy=5 => 1) It is not sufficient definitely. 2) x = 1, y = 2 and x = 2, y = 5/2 We don’t have a unique solution. 1) & 2) We have the following cases. x = 1, y = 5 / x = 1, y = 5 / x = 5, y = 1 / x = 1, y = 5 All of them have xy = 4. Thus we have a unique solution. Both conditions together are sufficient. Ans: C
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Re: Math Revolution Approach (DS)
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10 Sep 2017, 18:23
[GMAT math practice question] If a, b, and c are different positive integers, what is the value of a+b+c? 1) a^2+b^2+c^2=14 2) ab+bc+ca=11 => Condition 1) We can assume a < b < c without loss of generality. The maximum value of c is 3 and c^2 = 9 a^2 + b^2 = 5. Then we have b = 2 and a = 1. a + b + c = 1 + 2 + 3 = 6 Condition 2) We can assume a < b < c without loss of generality. ab + bc + ca = (a+b)c + ab = 11 Since a + b >= 3, the maximum value of c = 3. If c = 3, ab + 3b + 3a = 11 or ab + 3a + 3b + 9 = 20. We have (a+3)(b+3) = 20. Then a = 1 and b = 2. Thus a + b + c = 1 + 2 + 3 = 6. Therefore the answer is D Ans: D
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Re: Math Revolution Approach (DS)
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13 Sep 2017, 00:14
[GMAT math practice question] If x^3y^4z^5<0, is xyz>0? 1) y<0 2) x<0 => x^3y^4z^5 < 0 is equivalent to xz < 0. Then the question xyz > 0 is equivalent to y < 0. The condition 1) is sufficient. And the condition 2) is not sufficient. Ans: A
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Re: Math Revolution Approach (DS)
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14 Sep 2017, 00:51
[GMAT math practice question] In the coordinate plane, a triangle ABC has 3 points A(1,0), B(2,0), and C(m,n). What is the area of the triangle ABC? 1) m=1 2) n=2 => The area of the triangle is (1/2)*1*n. Then the condition 2) is sufficient. Ans: B
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