The last blog post I wrote showed how modifiers can fool people on quant problems – here’s the link.
Several of my students who got the baseball problem from that post correct dismissed the issue entirely and scoffed at me for showing them such an “easy problem,” then inevitably missed a variant of the problem I’m about to show you. Try it for yourself, and watch out for the modifiers!
The town of Malmo, Sweden has only two late-night food options: Pizza and Kebab. All sellers of late-night food have either a street permit or a permanent store permit. 60% of all the late-night food sellers in Malmo are street vendors that serve Kebab; 20% of all the late-night food sellers who have a permanent store serve Pizza. If Malmo’s ratio of total street permits to total permanent store permits is exactly 7 to 3, what percentage of all late-night food sellers in Malmo serve pizza?
(If you’re not sure how to approach this problem, try brushing up on overlapping sets, covered in the Manhattan GMAT Word Problems strategy guide. Then come back and give it a shot.)
( *** SPOILER *** ) —————————
Did you choose (D)? Sorry, that’s not the right answer! But if you picked it, don’t beat yourself up: it’s a trap.
“60% of all the late-night food sellers in Malmo are street vendors that serve Kebab” means:
1 – Out of all food sellers (assume there are 100 food sellers in Malmo)
2 – 60% of those
3 – are street vendors AND serve Kebab
Therefore, 60 vendors are street vendors that serve Kebab.
However, “20% of all the late-night food sellers who have a permanent store serve Pizza” means something DIFFERENT:
1 – Out of ONLY the permanent store vendors (of which there are 30 – we know that from the 7:3 ratio and our 100-vendor total assumption)
2 – 20% of those
3 – serve Pizza
Therefore, only 6 (20% of 30) vendors are permanent vendors that serve pizza, NOT 20! This is the critical step to understand. Whenever the GMAT mentions a percentage, there are two quantities involved: the part and the whole. In the first case, the whole is all vendors. But in the second case, the whole is restricted by the MODIFIER “who have a permanent store.” The problem is difficult largely because humans have a tendency to ignore modifiers that come at the end of long sentences. Be extra diligent on these types of word problems, especially ones involving many different percentages! Often the GMAT will trap you by showing you percentages of different wholes. When the different wholes are distinguished only by a modifier, the change can be very difficult to spot. Be sure you always know what you are taking a percentage of!
The correct answer is (B). If you missed it, try and work out the correct version on your own (I’m purposefully not giving a complete solution here), and use the comment section if you need help!
There’s one final thing I’d like you to take away from the Malmo problem above and the baseball problem in my previous post: when you see a hard problem, try and relate it to an easy one! The best GMAT students see the connection between the Malmö problem and the baseball problem, because they didn’t dismiss the baseball problem just because it was “easy.”