![\"c-trap\"](\"\/\/manhattanprep.com\/gmat\/wp-content\/uploads\/sites\/18\/2014\/04\/c-trap.png\")
Have you heard of the C-Trap? I\u2019m not going to tell you what it is yet. Try this problem from GMATPrep\u00ae first and see whether you can avoid it<\/p>\nHave you heard of the C-Trap? I\u2019m not going to tell you what it is yet. Try this problem from GMATPrep\u00ae first and see whether you can avoid it<\/p>\n
* \u201cIn a certain year, the difference between Mary\u2019s and Jim\u2019s annual salaries was twice the difference between Mary\u2019s and Kate\u2019s annual salaries. If Mary\u2019s annual salary was the highest of the 3 people, what was the average (arithmetic mean) annual salary of the 3 people that year?<\/p>\n
\u201c(1) Jim\u2019s annual salary was $30,000 that year.<\/p>\n
\u201c(2) Kate\u2019s annual salary was $40,000 that year.\u201d<\/p>\n
I\u2019m going to do something I normally never do at this point in an article: I\u2019m going to tell you the correct answer. I\u2019m not going to type the letter, though, so that your eye won\u2019t inadvertently catch it while you\u2019re still working on the problem. The correct answer is the second of the five data sufficiency answer choices.<\/p>\n
How did you do? Did you pick that one? Or did you pick the trap answer, the third one?<\/p>\n
Here\u2019s where the C-Trap gets its name: on some questions, using the two statements together will be sufficient to answer the question. The trap is that using just one statement alone will also get you there\u2014so you can\u2019t pick answer (C), which says that neither statement alone works.<\/p>\n
In the trickiest C-Traps, the two statements look almost the same (as they do in this problem), and the first one doesn\u2019t work. You\u2019re predisposed, then, to assume that the second statement, which seemingly supplies the \u201csame\u201d kind of information, also won\u2019t work. Therefore, you don\u2019t vet the second statement thoroughly enough before dismissing it\u2014and you\u2019ve just fallen into the trap.<\/p>\n
How can you dig yourself out? First of all, just because two statements look similar, don\u2019t assume that they either both work or both don\u2019t. The test writers are really good at setting traps, so assume nothing.
\n
\nSecond, imagine that you\u2019re teaching your 10-year-old niece how to do algebra. She\u2019s never done this before but she\u2019s pretty bright. She understands your explanation of what variables are and how they work. She knows that, if you give her an equation with 3 variables, and then give her values for 2 of those variables, she\u2019ll be able to solve for the third one. What answer is she going to pick on the above problem?<\/p>\n
Hmm. She\u2019d pick (C) also, since that gives her values for two of the three variables in the equation that she can write from the question stem.<\/p>\n
It\u2019s obvious, in fact, that using the two statements together will allow you to find all three salaries, in which case you can average them. In the test-prep world, this is what\u2019s known as a Too Good To Be True answer. If your 10-year-old niece, who just learned algebra, could get to the same answer, then chances are you\u2019re falling into a trap. Stop, take a deep breath, and scrutinize those statements individually!<\/p>\n
Here\u2019s how to solve the problem.<\/p>\n
Step 1: Glance Read Jot<\/i><\/p>\n
Take a quick glance; what have you got? DS. Story problem: understand the story before writing.<\/p>\n
The question asks for the average of the three salaries. What do you actually need to know in order to find an average? Right, the sum. So can you find the sum of the three salaries?<\/p>\n
Jot that on your scrap paper: M<\/i> + J<\/i> + K<\/i> = ?<\/p>\n
Step 2: Reflect Organize<\/i><\/p>\n
The first sentence provides an equation, so translate it. (Note that the second sentence says Mary\u2019s salary is the highest.)<\/p>\n
The positive difference between Mary\u2019s and Jim\u2019s salaries has to be M<\/i> \u2013 J<\/i>, since M<\/i> is larger. Likewise, the positive difference between Mary\u2019s and Kate\u2019s salaries has to be M<\/i> \u2013 K<\/i>, since M<\/i> is larger.<\/p>\n
Here\u2019s the translated formula:<\/p>\n
M<\/i> \u2013 J<\/i> = 2(M<\/i> \u2013 K<\/i>)<\/p>\n
Step 3: Work<\/i><\/p>\n
By itself, that doesn\u2019t look very helpful, but anytime DS gives you a formula that isn\u2019t simplified, simplify it. Multiply out the right-hand side and also get \u201clike\u201d variables together:<\/p>\n
M<\/i> \u2013 J<\/i> = 2(M<\/i> \u2013 K<\/i>)<\/p>\n
M<\/i> \u2013 J<\/i> = 2M<\/i> \u2013 2K<\/i><\/p>\n
– J<\/i> = M<\/i> \u2013 2K<\/i><\/p>\n
Notice two things: first, negatives are annoying. Second, this formula (so far) doesn\u2019t look anything like the question: M<\/i> + J<\/i> + K<\/i> = ?<\/p>\n
Is there any way to remedy those two things?<\/p>\n
Move the \u2013J<\/i> over: 0 = M<\/i> \u2013 2K<\/i> + J<\/i>.<\/p>\n
Notice that 2K<\/i> is never going to fit the question, which has only K<\/i>. Move that away from the others: 2K<\/i> = M<\/i> + J<\/i>.<\/p>\n
Interesting. The right-hand side now matches part of the question. In fact, you could substitute:<\/p>\n
M<\/i> + J<\/i> + K<\/i> = ?<\/p>\n
2K<\/i> = M<\/i> + J<\/i><\/p>\n
Therefore, the question becomes 2K<\/i> + K<\/i> = ?<\/p>\n
If you know what K<\/i> is\u2014only K<\/i>!\u2014 then you can solve. (Note: we call this process Rephrasing<\/i>. Use the information given in the question stem to rephrase the question in a more simplified form.)<\/p>\n
\u201c(1) Jim\u2019s annual salary was $30,000 that year.\u201d<\/p>\n
J<\/i> = 30,000. If you plug that into M<\/i> + J<\/i> + K<\/i> = ?, it isn\u2019t sufficient. If you plug that into 2K<\/i> = M<\/i> + J<\/i>, you get 2K<\/i> = M<\/i> + 30,000, which still isn\u2019t sufficient. Knowing only J<\/i> doesn\u2019t get you very far. This statement is not sufficient; eliminate answers (A) and (D).<\/p>\n
\u201c(2) Kate\u2019s annual salary was $40,000 that year.\u201d<\/p>\n
Bingo! If you know Kate\u2019s salary, then you know the sum of all three. This statement is sufficient to answer the question.<\/p>\n
The correct answer is (B).<\/p>\n
If you don\u2019t rephrase up front, and instead go through all of the work of plugging in the values for statements (1) and (2), then you may still discover the correct answer. You\u2019ll take longer, though. You may also fall into the trap of assuming that statement (2) won\u2019t work because it looks so very similar to statement (1) and that one didn\u2019t work.<\/p>\n
Key Takeaways: Data Sufficiency<\/b><\/p>\n
(1) Don\u2019t just write down the information in the question stem, shrug, and go straight to the statements. Push yourself to try to rephrase<\/i> the question before you go to the statements.<\/p>\n
(2) Use standard math steps and<\/i> your test-taker savvy to help you know how to simplify. It\u2019s standard algebra to try to get \u201clike\u201d variables together in equations. A negative sticking out in front of an equation is ugly, so that was clue #2. Finally, you\u2019re ultimately trying to match the information in the question (M<\/i> + J<\/i> + K<\/i> = ?), so try to rearrange your rephrased equation to match the question as much as possible. Then see whether you can substitute in to make that question simpler!<\/p>\n
(3) Keep an eye out for Too Good to Be True answers. If an answer seems pretty obvious, then there\u2019s a good chance you\u2019re falling into a trap!<\/p>\n
* GMATPrep\u00ae questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.<\/p>\n
\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"
Have you heard of the C-Trap? I\u2019m not going to tell you what it is yet. Try this problem from GMATPrep\u00ae first and see whether you can avoid it * \u201cIn a certain year, the difference between Mary\u2019s and Jim\u2019s annual salaries was twice the difference between Mary\u2019s and Kate\u2019s annual salaries. If Mary\u2019s annual […]<\/p>\n","protected":false},"author":6,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[15,2,8,9],"tags":[233,241,346,347,370,392,734,736],"yst_prominent_words":[],"class_list":["post-7133","post","type-post","status-publish","format-standard","hentry","category-data-suff","category-how-to-study","category-quant-on-gmat","category-taking-the-gmat","tag-gmat","tag-gmat-c-trap","tag-gmat-strategies","tag-gmat-strategy","tag-gmat-testing-strategy","tag-graduate-management-admission-test","tag-test-strategy","tag-test-taking-strategy"],"_links":{"self":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/7133","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/comments?post=7133"}],"version-history":[{"count":1,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/7133\/revisions"}],"predecessor-version":[{"id":17441,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/posts\/7133\/revisions\/17441"}],"wp:attachment":[{"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/media?parent=7133"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/categories?post=7133"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/tags?post=7133"},{"taxonomy":"yst_prominent_words","embeddable":true,"href":"https:\/\/www.manhattanprep.com\/gmat\/wp-json\/wp\/v2\/yst_prominent_words?post=7133"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}