Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Jun 0408:30 AM PDT
-09:30 AM PDT
For most test takers, Data Insights is the most challenging section on the GMAT, with test takers scoring several points lower on average on DI than on Quant or Verbal and completing the section with less time to spare.
May 2910:00 AM IST
-11:00 PM IST
Start your journey with a fully customized action plan and work with a dedicated mentor to achieve a 735+ score.- Jun 03
08:30 AM PDT
-09:30 AM PDT
In Episode 7 of our GMAT Ninja CR series, we are rounding up the oddballs, the misfits, and the format-benders: EXCEPT, Fill-In-The-Blanks, and other unusual Critical Reasoning question types. When you see a question that ends with a literal blank line - Jun 10
06:00 AM PDT
-06:15 PM PDT
Register for the GMAT Club Virtual MBA Spotlight Fair – the world’s premier event for serious MBA candidates. This is your chance to hear directly from Admissions Directors at nearly every Top 30 MBA program..
23 Aug 2024, 09:10
Kudos
Bookmarks
If \(x\) and \(y\) are integers \(35x = 69y\), which of the following must be true?
I. \(x > y\)
II. \(\frac{y}{7}\) is an integer
III. \(\frac{x}{23}\) is an integer
A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III
I. \(x > y\)
II. \(\frac{y}{7}\) is an integer
III. \(\frac{x}{23}\) is an integer
A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III
23 Aug 2024, 09:11
Kudos
Bookmarks
Official Solution:
If \(x\) and \(y\) are integers \(35x = 69y\), which of the following must be true?
I. \(x > y\)
II. \(\frac{y}{7}\) is an integer
III. \(\frac{x}{23}\) is an integer
A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III
It is important to note that the problem does not specify that \(x\) and \(y\) are necessarily positive. Therefore, when evaluating each option, it is essential to keep in mind that these variables may take non-positive values!
I. \(x > y\).
This statement is not always true, as \(x\) and \(y\) are not necessarily positive. For instance, consider \(x = -69\) and \(y=-35\), or \(x = 0\) and \(y=0\).
II. \(\frac{y}{7}\) is an integer
From \(35x = 69y\), we can infer that since the left-hand side, \(35x = 7(5x)\), is a multiple of 7, the right-hand side, \(69y\), must also be a multiple of 7. Since 69 is not a multiple of 7 (prime number), \(y\) must be, making \(\frac{y}{7}\) an integer. Hence, this option is always true.
III. \(\frac{x}{23}\) is an integer
From \(35x = 69y\), we can infer that since the right-hand side, \(69y = 23(3y)\), is a multiple of 23, the left-hand side, \(35x\), must also be a multiple of 23. Since 35 is not a multiple of 23 (prime number), \(x\) must be, making \(\frac{x}{23}\) an integer. Hence, this option is always true.
Answer: D
If \(x\) and \(y\) are integers \(35x = 69y\), which of the following must be true?
I. \(x > y\)
II. \(\frac{y}{7}\) is an integer
III. \(\frac{x}{23}\) is an integer
A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III
It is important to note that the problem does not specify that \(x\) and \(y\) are necessarily positive. Therefore, when evaluating each option, it is essential to keep in mind that these variables may take non-positive values!
I. \(x > y\).
This statement is not always true, as \(x\) and \(y\) are not necessarily positive. For instance, consider \(x = -69\) and \(y=-35\), or \(x = 0\) and \(y=0\).
II. \(\frac{y}{7}\) is an integer
From \(35x = 69y\), we can infer that since the left-hand side, \(35x = 7(5x)\), is a multiple of 7, the right-hand side, \(69y\), must also be a multiple of 7. Since 69 is not a multiple of 7 (prime number), \(y\) must be, making \(\frac{y}{7}\) an integer. Hence, this option is always true.
III. \(\frac{x}{23}\) is an integer
From \(35x = 69y\), we can infer that since the right-hand side, \(69y = 23(3y)\), is a multiple of 23, the left-hand side, \(35x\), must also be a multiple of 23. Since 35 is not a multiple of 23 (prime number), \(x\) must be, making \(\frac{x}{23}\) an integer. Hence, this option is always true.
Answer: D
04 Sep 2024, 00:37
Kudos
Bookmarks
pls provide difficulty level for this question
