Fractions problem

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

manik11: Master | Next Rank: 500 Posts; Posts: 113; Joined: Wed Dec 07, 2011 7:20 am; Thanked: 3 times

Fractions problem

by manik11 » Thu Feb 18, 2016 5:30 am

If x and y are positive integers, does X/Y = 7/9?

1. X=103
2. 11/13 < X/Y < 8/9

OA : D

Hi Experts! I don't understand how statement 1 could be sufficient, Its been a common pattern in most of the DS problems I've solved so far that when the prompt involves two variables and the statement doesn't say anything about one of the variables, its almost always insufficient.
I would really appreciate if you guys could link some similar problems in you replies.

Thanks!

Quote

Source: Beat The GMAT — Data Sufficiency | Thu Feb 18, 2016 5:30 am

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Thu Feb 18, 2016 9:15 am

Hi manik11,

When dealing with certain DS questions, your 'gut instinct' will be incorrect, so you have to get in the habit of doing a certain amount of work to actually prove whether you're correct or not (otherwise you might pick one of the wrong answers and not even realize it).

The prompt tells us that X and Y are POSITIVE INTEGERS. That is an interesting 'restriction.' We're asked if X/Y = 7/9.

1) X = 103

This Fact gives us the value of X, so your instinct is probably to say "I don't know the value of Y, so this is probably insufficient....' Remember the restriction that X and Y had to be INTEGERS though. Is there ANY possible INTEGER value for Y that would make 103/Y = 7/9? How long will it take you to prove it?

You're going to find that if Y must be a positive integer, then there is no possible value for Y that makes 103/Y = 7/9, so the answer to the question is ALWAYS NO and Fact 1 is SUFFICIENT.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Quote

Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pm; Location: East Bay all the way; Thanked: 625 times; Followed by:119 members; GMAT Score:780

by Matt@VeritasPrep » Thu Feb 18, 2016 6:23 pm

x/y = 7/9

gives us

9x = 7y

Since these are both positive integers, we now have

x = a multiple of 7
y = a multiple of 9

But 103 isn't a multiple of 7! So x can't be a multiple of 7, and x/y can't be 7/9.

Save $100 on any VP online course!

Quote

MartyMurray: Legendary Member; Posts: 2135; Joined: Mon Feb 03, 2014 9:26 am; Location: https://martymurraycoaching.com/; Thanked: 955 times; Followed by:140 members; GMAT Score:800

by MartyMurray » Thu Feb 18, 2016 7:59 pm

manik11 wrote:Hi Experts! I don't understand how statement 1 could be sufficient, Its been a common pattern in most of the DS problems I've solved so far that when the prompt involves two variables and the statement doesn't say anything about one of the variables, its almost always insufficient.

The pattern you mentioned tends to show up in more basic DS questions, and assuming that it will hold can be risky. For one thing, anyone writing a question knows that people commonly look for equations containing all of the variables. So a good way to write a trick question is to write it in such a way that it's solvable via using something that does not include all of the variables.

Here are a couple of questions that can be answered by using statements that do not include all of the variables.

1) What is the value of (w + x)(y + z)?

(1) 3w + 3x = 51

(2) yÂ² + 2yz + zÂ² = 0

2) An auto dealership has multiple departments. Each of the departments has a manager, each department has multiple employees who work with the manager, and each department has the same number of of people in it. If there are only department managers and other department employees working at the dealership, and if there are fewer than 25 employees at the dealership, how many employees does the dealership have?

(1) The ratio of managers to non manager employees is 1:7.

(2) There are 21 non manager employees at the dealership.

The OA to question 1 is B.

The OA to question 2 is B.

Marty Murray
Perfect Scoring Tutor With Over a Decade of Experience
MartyMurrayCoaching.com
Contact me at [email protected] for a free consultation.

Quote

MartyMurray: Legendary Member; Posts: 2135; Joined: Mon Feb 03, 2014 9:26 am; Location: https://martymurraycoaching.com/; Thanked: 955 times; Followed by:140 members; GMAT Score:800