a\u2019<\/em> through \u2018e\u2019 with a line at the top to write down what the question is asking for.<\/p>\n\n\n\n\\(f(x^2)=?\\)<\/p>\n\n\n\n
a. \\(1-x^4=1-(3^2)^2=1-81=-80\\)<\/p>\n\n\n\n
b. <\/p>\n\n\n\n
c. <\/p>\n\n\n\n
d. <\/p>\n\n\n\n
e. <\/p>\n\n\n\n
In this case, we have relatively complex expressions so we are not going to write them down. We skip to the end and see that we are being asked for the value of \\(f(x^2)\\).<\/p>\n\n\n\n
In general, it is best to set up the technical approach first. We know that we nest the functions.<\/p>\n\n\n\n
We know that if we are looking for \\(f(x^2)\\), that stands in for the \\(x\\).<\/p>\n\n\n\n
Therefore, \\(f(x^2)=1-(x^2)^2=1-x^4\\)<\/p>\n\n\n\n
The correct answer is choice A.<\/p>\n\n\n\n
But if we didn\u2019t set up the technical approach, we can still solve the problem by just plugging in easy values. In this case, we have \\(1-(x^2)\\), and we have 1s and 2s and 4s, so we want to avoid these numbers that are already in the problem so let\u2019s say \\(x=3\\)<\/p>\n\n\n\n
If \\(x=3\\rightarrow x^2=9\\) since \\(f(x)=1-x^2\\rightarrow f(x)=1-9 \\rightarrow f(x) = -8\\) therefore,<\/p>\n\n\n\n
$$\\begin{align*}f(x^2)&=1-92\\\\ f(x^2)&=1-81\\\\ f(x^2)&=-80\\end{align*}$$ <\/p>\n\n\n\n
If we plug in our values of x<\/em> we should be able to get a result of -80. Remember \\(x=3\\).<\/p>\n\n\n\nLooking at choice A, on our scratch pad, \\(1-x^4=1-(3^2)^2=1-81=-80\\). <\/p>\n\n\n\n
On the exam go on and test the rest of them to make sure there is no duplicate. Still, if we take a look at choice B, the answer > 0 so it is obviously incorrect. The same goes for choice C. The same applies to choices D and E.<\/p>\n\n\n\n
We can solve this quickly through modeling. We know -80 is our result, we just need to find out what answer choices if we plug in 3 we will end up with -80 as our result.<\/p>\n\n\n\n
<\/span>Example 2<\/span><\/h3>\n\n\n\nFor any two unique positive integers \\(a\\) and \\(b\\), \\(a\u2302b\\) represents the greatest common factor of \\(a\\) and \\(b\\). If \\(x\\)y\\), what is the value of \\(x\u2302y\\)?<\/p>\n\n\n\n
(1) \\(x=16\\)<\/p>\n\n\n\n
(2) \\(y=17\\)<\/p>\n\n\n\n
We start with what we know. We know that for any two unique integers a and b, a \u2260 b; a > 0; b > 0; \\(a\u2302b=GCF\\) of \\(a\\) and \\(b\\).<\/p>\n\n\n\n
\\(x<y\\). the question is asking for the value of \\(x\u2302y\\).<\/p>\n\n\n\n
we need to know the GCF of \\(x\\) and \\(y\\).<\/p>\n\n\n\n
(i) \\(x=16\\)<\/p>\n\n\n\n
if \\(x = 16\\) and \\(y = 32\\), the greatest common factor 16. But if \\(y = 30\\) then the GCF is just going to be 2. We\u2019ve got multiple possible outcomes and therefore condition (1) by itself is not sufficient. We are left with BC&E.<\/p>\n\n\n\n
(ii) \\(y=17\\)<\/p>\n\n\n\n
if \\(y = 17\\), we know that \\(x < y\\). we look at the factors of 17. They are 1 and 17. And since \\(X < 17\\). The GCF of 17 and anything less than it is 1. That gives us everything that we need to solve the problem and makes condition (2) by itself sufficient. We can select choice B.<\/p>\n\n\n\n
Both of these examples at first glance seem very complex, you wonder what these functions and symbols are. But that is the exam taking advantage of your assumptions and trying to make you think things are harder than they are. That is a very important skill for you to have as a manager which is why this is a common tactic of the executive assessment.<\/p>\n\n\n\n
Remain calm, work through the steps of the problem, and these weird functions and symbols will become part of your path to getting the score you need to attend your target program.<\/p>\n\n\n\n
Practice more of these problems on your own to improve your skills for your test date. <\/p>\n","protected":false},"excerpt":{"rendered":"
This is one of the higher-difficulty questions that you will find on the executive assessment, but honestly, the test tries to shock and awe you into thinking something is harder than it really is. Basic Function Notation $$f(X)=\\frac{x+1}{x}$$ Functions defined…<\/p>\n","protected":false},"author":7,"featured_media":10805,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[201,73],"tags":[],"class_list":["post-10797","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gmat","category-study-tips","blog-post","animate"],"acf":[],"post_mailing_queue_ids":[],"_links":{"self":[{"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/posts\/10797","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/comments?post=10797"}],"version-history":[{"count":7,"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/posts\/10797\/revisions"}],"predecessor-version":[{"id":10804,"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/posts\/10797\/revisions\/10804"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/media\/10805"}],"wp:attachment":[{"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/media?parent=10797"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/categories?post=10797"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/tags?post=10797"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}