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## IR Explained: Q32: Daily Shoppers

###### August 22, 2012

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*This post is part of a series--IR Explained--that walks through the sample Integrated Reasoning questions provided in the latest edition of the GMAT Official Guide.*

This Graphics Interpretation question has a particularly thorny setup. For each of three days, we're given the breakdown of a retailer's customers based on their behavior. But for each day, we are only discussing those customers who came to the retailer on day 1.

In other words, the Day 2 shoppers represented on the graph are only those shoppers who came to the retailer on Day 2 *after* doing so on Day 1, as well.

Looking at the three types of behaviors represented in each bar, the logic becomes clearer. On Day 1, 60% of shoppers purchased a different item and did not return that week. 25% didn't purchase anything and returned the next day. The remaining 15% didn't purchase anything and did not return.

Thus, 25% of Day 1 shoppers returned the next day; the other 75% did not return either Day 2 or Day 3 (or Day 4, for that matter).

The graph, then, is misleading. While it shows Day 1, Day 2, and Day 3 as bars of equal height, the number of shoppers represented on day 2 is only a quarter the number of those on day 1.

Question 32A zeroes in on this source of complexity. What percentage of Day 1 shoppers returned on Day 3? We know that 25% of Day 1 shoppers returned on Day 2, and 75% of Day 1 shoppers did not return all week. Thus, any Day 1 shopper who returned on Day 3 must have also returned on Day 2.

The bar for Day 2 shows us that 19% of shoppers on Day 2 returned the next day. (The other 81%, whether they made a purchase or not, did not return.) Thus, if 25% of Day 1 shoppers returned on Day 2, and 19% of Day 2 shoppers returned on Day 3, then percentage of *Day 1* shoppers who returned on Day 3 is (25%)(19%) = (.25)(.19), or about 5%. That's **Between 1 and 10**.

In 32B, you are asked to compare the amount that Day 1 shoppers paid for alternate items to the amount that Day 1 shoppers *would have* paid for the original, out-of-stock item had they all purchased it.

Say that there were 100 Day 1 shoppers and the original item cost $10. If all the shoppers had been able to purchase it, they would have spent $1000.

Instead, only 60% (60) Day 1 shoppers purchased an alternate item. We're told from the introductory paragraph that the substitute item cost, on average, 30% more. That's $13 instead of $10.

Thus, 60 shoppers paid $13 each, for a total of $780. Compared to $1000, $780 is **78%**, our answer.

*Stay tuned (or subscribe) for more Integrated Reasoning explanations*

**About the author:** *Jeff Sackmann has written many
GMAT preparation books, including the popular Total GMAT Math,
Total GMAT Verbal, and GMAT 111. He has also created
explanations for problems in The Official Guide, as well as
1,800 practice GMAT math questions.*

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