ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

More Help To Ace Your SAT Math Test, Tip #4

Updated on November 29, 2014

Previous hubs have introduced the technique of applying actual numbers, then showed how to use this technique on problems that have equations – one-variable equations, multiple-variable equations, and equations in the answer choices. It’s time to move on to inequalities.

The key to applying actual numbers to inequalities is to be sure that the answer choice (1) includes everything it should and (2) excludes everything it should. Let’s take a look at a problem considered to be relatively hard.

Applying Actual Numbers to an Inequality


One of the things that makes this problem hard, quite frankly, is the deer-in-the-headlights effect that parabolas (the curved shape on the graph) have on some test takers. So the first thing to do is to overcome that feeling! The SAT never asks you to actually come up with a parabola’s equation. Instead, your job will be simply to make sense of what’s on the graph. And as long as you remember that the x value corresponds to how far a point is to the left or right, while the y value corresponds to how high or low a point is, this task won’t be all that difficult after all.

For starters, the parabola is labeled y = g(x), and the straight line is labeled y = f(x). This means that g(x) and f(x) correspond to the y value (not the x value) of the parabola and line, respectively. So when the question asks where g(x) > f(x), it just means, “Where is the y value of the parabola greater (that is, higher) than the y value of the line?” Let’s pick an obvious place where this is the case. How about where x = -2? Cross off each answer choice that does not include -2:

(A) -6 < x < -3 only ✗
(B) -3 < x < 0 only ✓
(C) 0 < x < 3 only ✗
(D) 3 < x < 6 only ✗
(E) -6 < x < -3 and 0 < x < 3 ✗

Cross off answer choices that exclude included stuff, or include excluded stuff,

Lo and behold, only one answer choice survives! Just for the sake of practice, though, let’s suppose that answer choice (E) read:

(E) -6 < x < 0 only

This inequality includes -2, so it would not have been eliminated in the previous step. In fact, if I pick any x value for which the parabola is higher than the straight line, (E) would still survive. At this point, then, I would need to pick a value that clearly should not be included. Since I need to choose between (B) and the new (E), I’ll pick a value that is included in one and not in the other. How about -4? Looking at the graph, I can see that -4 should be excluded, but the new (E) includes it. So I would eliminate (E) because it includes too much.

Inequalities versus Equations

The strategy I’ve been discussing works with inequalities a little differently than it does with equations. Although it occasionally happens, as above, that picking and applying one number gets you to one remaining answer choice, be prepared to pick and apply more than one number. Good numbers to pick will be:

  • clearly within the given range (like -2 above)
  • clearly outside the given range (like -4 above)
  • near the the cut-off points for the range (I may have picked -2.9 above if I needed to)

More to come: I’ll be looking at two more kinds of SAT problems in the next two hubs. Notice that each of these hubs also applies to math problems on the ACT, GRE and GMAT. After the last two SAT hubs, the next subjects I plan to tackle are the special – and especially challenging – formats on the GRE and GMAT, and how to apply actual numbers to those kinds of problems. Those of you puzzled by Quantitative Comparison and Data Sufficiency: Help is on its way!


    0 of 8192 characters used
    Post Comment

    No comments yet.


    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

    For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at:

    Show Details
    HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
    LoginThis is necessary to sign in to the HubPages Service.
    Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
    AkismetThis is used to detect comment spam. (Privacy Policy)
    HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
    HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
    Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
    CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
    Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the or domains, for performance and efficiency reasons. (Privacy Policy)
    Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
    Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
    Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
    Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
    Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
    VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
    PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
    Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
    MavenThis supports the Maven widget and search functionality. (Privacy Policy)
    Google AdSenseThis is an ad network. (Privacy Policy)
    Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
    Index ExchangeThis is an ad network. (Privacy Policy)
    SovrnThis is an ad network. (Privacy Policy)
    Facebook AdsThis is an ad network. (Privacy Policy)
    Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
    AppNexusThis is an ad network. (Privacy Policy)
    OpenxThis is an ad network. (Privacy Policy)
    Rubicon ProjectThis is an ad network. (Privacy Policy)
    TripleLiftThis is an ad network. (Privacy Policy)
    Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
    Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
    Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
    Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
    ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
    Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)