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For integers x and y, if 91x = 8y, which of the following must be true
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22 Sep 2015, 02:05
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Re: For integers x and y, if 91x = 8y, which of the following must be true
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22 Sep 2015, 03:04
Bunuel wrote: For integers x and y, if 91x = 8y, which of the following must be true?
I. y > x II. y/7 is an integer III. The cube root of x is an integer
A) I only B) II only C) III only D) I and II E) II and III
Kudos for a correct solution. Statement 1: y>x When y=x=0, equation holds but y is not greater than x When x=8 and y=91, equation again holds but x>y NOT TRUE Statement 2: y/7 is an integer Since x and y are integers, 91x and 8y must also be integers. It is given that 91x=8y or 13*7*x = 8 y or 13x = 8y/7 To balance the equation, y/7 must be an integer TRUE Statement 3: The cube root of x is an integer x can be equal to 2*2*2*3 and for this value of x,y will be 13*7*3 So, x may or may not be a cube root. NOT TRUE Answer:B




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For integers x and y, if 91x = 8y, which of the following must be true
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22 Sep 2015, 03:01
Bunuel wrote: For integers x and y, if 91x = 8y, which of the following must be true?
I. y > x II. y/7 is an integer III. The cube root of x is an integer
A) I only B) II only C) III only D) I and II E) II and III
Kudos for a correct solution. Given 91*x=8*y It can be equal when x = 8 or 8 and y = 91 or 91 So Statement (I) y < x if we take x = 8 and y =91 but y > x if we take x = 8 and y = 91, so (I) is not true always Statement (2) in any case91/7 or 91/7 is an integer that is 13 or 13. So it is true Statement (3) cube root of 8 or 8 is 2 and 2 respectively. So it is true always. So IMO answer is E
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Re: For integers x and y, if 91x = 8y, which of the following must be true
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22 Sep 2015, 14:51
1) 91 * 8 = 8 * 91, y > x 91 * 8 = 8 * 91, y < x False
2) The valid numbers for x 0, and plus/minus multiples of 8. Therefore, the valid numbers for y are 0 and multiples of +91, which are divisible by 3. True
3) Consider the case where x = 8, y = 81. The root of x is not an integer, and rooting it again does not make it an integer. False
Answer B



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Re: For integers x and y, if 91x = 8y, which of the following must be true
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27 Sep 2015, 10:08
Bunuel wrote: For integers x and y, if 91x = 8y, which of the following must be true?
I. y > x II. y/7 is an integer III. The cube root of x is an integer
A) I only B) II only C) III only D) I and II E) II and III
Kudos for a correct solution. VERITAS PREP OFFICIAL SOLUTION:Solution: B. Statement 1 is not necessarily true. x could equal 8 and y could equal 91, for example, in which case the equation holds but x > y” title=”x > y”/>. Statement 2 is true: for <img src= to equal 91x, then the prime factorization: 2*2*2*y = 13*7*x. y must then be able to account for the prime factor of 7 on the other side of the equation. And statement 3 is not necessarily true. While x must account for the factors 2*2*2, it could also include a noncubed factor as well. For example, x could be 2*2*2*5 and y could be 13*7*5. The equation would hold because the extra 5 is accounted for on both sides. x MUST account for 2*2*2, but need not be limited to just that, as x and y could have duplicate factors on either side. Beware the statements that look very likely to be true when you face these “must be true” problems – the GMAT is a master of misdirection.
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For integers x and y, if 91x = 8y, which of the following must be true
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02 Jul 2016, 12:27
Hi Bunuel,
I have one doubt in this question. Why can't y be a factor of 13. If Y is a factor of 13, it will still solve the equation. Can you please explain why y/7 will be an integer.
Thanks.



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Re: For integers x and y, if 91x = 8y, which of the following must be true
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03 Jul 2016, 03:08



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Re: For integers x and y, if 91x = 8y, which of the following must be true
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25 Sep 2017, 15:40
Bunuel wrote: For integers x and y, if 91x = 8y, which of the following must be true?
I. y > x II. y/7 is an integer III. The cube root of x is an integer
A) I only B) II only C) III only D) I and II E) II and III Without actually solving the equation algebraically, we can see that x could be 8 and y could be 91, since 91(8) = 8(91). However, this is not the only possibility. We see that x could be 0 and y could be 0, since 91(0) = 8(0), or x could be 8 and y could be 91, since 91(8) = 8(91). In any event, we see that x is a multiple of 8 (including 0 and the negative multiples) and y is a multiple of 91 (including 0 and the negative multiples). Let’s analyze each Roman numeral: I. y > x Since both x and y could be 0, y is not necessarily greater than x. Roman numeral I is not true. II. y/7 is an integer Since y is a multiple of 91, y/7 is an integer. Roman numeral II must be true. III. The cube root of x is an integer We’ve mentioned that x is a multiple of 8. If x = 8, then the cube root of x is an integer. However, if x = 16, then the cube root of x is not an integer. Roman numeral III is not true. Answer: B
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Re: For integers x and y, if 91x = 8y, which of the following must be true
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27 Sep 2018, 02:56
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Re: For integers x and y, if 91x = 8y, which of the following must be true &nbs
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