Is Statement one sufficient?

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

OluwaseunMakinde: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Mon May 09, 2016 7:58 am

Is Statement one sufficient?

by OluwaseunMakinde » Tue May 17, 2016 3:20 am

Hello house,

I came across this question in the 2016 OG and the answer was given as D. In my opinion the answer is B, Please help determine if statement one is sufficient.

Max has $125 consisting of bills each worth either $5 or $20. How many bills
worth $5 does Max have?
(1) Max has fewer than 5 bills worth $5 each.
(2) Max has more than 5 bills worth $20 each.

Quote

Source: Beat The GMAT — Data Sufficiency | Tue May 17, 2016 3:20 am

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 » Tue May 17, 2016 7:41 am

The total quantity of money Max has is $125.

If he has fewer than 5 $5 bills, then he has less than $25 in $5 bills. The next multiple of 5 below 25 is 20.

125-20 = 105

5 x 20 = 100

So 5 $20 bills won't get him to the total if he has fewer than 5 $5 bills.

Now what do you think about Statement 1?

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

Quote

GMAT/MBA Expert

ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pm; Thanked: 1443 times; Followed by:247 members

Is Statement one sufficient?

by ceilidh.erickson » Tue May 17, 2016 7:54 am

This question is testing INTEGER CONSTRAINTS. If we have $5 bills and $20 bills, we have to have a whole number of each.

With these types of problems in DS, it's useless to set up an equation. 5x + 20y = 125 will look unsolvable, as algebraic equations can't account for integer constraints. Instead, make a CHART:

Start with the maximum # of 20's - it's usually easier to start with the bigger one:

You don't have to fill in everything, but just enough to notice patterns to start. Then, fill in the # of 5's that would add up to $125 total:

Now when you're looking at the statements, here's your goal:
See if the statements restrict it to a single scenario in your chart.

(1) Max has fewer than 5 bills worth $5 each.
Cross off any scenarios in your chart that don't apply: