PrepLattice is an independent test-preparation service and is not affiliated with or endorsed by GMAC, the organization that administers the GMAT. GMAT and GMAT Focus are trademarks of GMAC, used here only to name the exam this question is designed to prepare you for.
A logistics dispatcher's routing software flags a truck for inspection whenever the truck's recorded distance x (in miles) satisfies |2x − 20| = x − 4. What is the sum of all values of x that the software flags?
Five fresh questions every day, your progress tracked, every miss explained. Free with an account.
Correct answer
D
Solve an absolute-value equation by splitting into its two sign cases, then check each candidate against the equation. The bars around 2x − 20 mean the quantity inside could be positive or negative, so write two cases.
Case 1 (inside is positive or zero): 2x − 20 = x − 4. Subtract x from both sides: x − 20 = −4, so x = 16. Check: |2(16) − 20| = |12| = 12, and 16 − 4 = 12. The two sides match, so x = 16 is valid.
Case 2 (inside is negative): 2x − 20 = −(x − 4) = −x + 4. Add x to both sides: 3x − 20 = 4, so 3x = 24 and x = 8. Check: |2(8) − 20| = |−4| = 4, and 8 − 4 = 4. The two sides match, so x = 8 is valid.
both cases give a genuine solution, so the truck is flagged at x = 16 and at x = 8. The sum is 16 + 8 = 24, which is (D).
Why the wrong choices are tempting: (C) 16 keeps only the positive case and forgets the negative case, a very common slip on absolute-value equations. (A) 8 makes the mirror-image mistake, keeping only the negative case. (B) 10 comes from setting the inside of the absolute value equal to zero (2x − 20 = 0); that is the point where the expression changes sign, not a solution to the equation. (E) 32 takes the positive-case root 16 and doubles it on the false idea that the answer must come in a symmetric pair of equal size. The only choice that correctly handles both sign cases and adds the two valid roots is (D) 24.
Pick the theme that suits how you work. You can change it anytime.