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14 Mar 2024, 02:53
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My answer for visual thinkers, similar to the Bunuel with the critical points
( I find useful to learn how to draw 1/x - with vertical and horizontal offsets - the same as known line equations and parabolas )
You can see the 4 different zones A,B, P, Q - sorry for the letters
the limits are (0,1) (1, something between 1 and 2)((something between 1 and 2, 2 )(2, inf)
GMAT-Club-Forum-167dfckl.png [ 267.01 KiB | Viewed 277 times ]
( I find useful to learn how to draw 1/x - with vertical and horizontal offsets - the same as known line equations and parabolas )
You can see the 4 different zones A,B, P, Q - sorry for the letters
the limits are (0,1) (1, something between 1 and 2)((something between 1 and 2, 2 )(2, inf)
Attachment:
GMAT-Club-Forum-167dfckl.png [ 267.01 KiB | Viewed 277 times ]
15 Jul 2025, 06:11
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Vavali
Here, Since we are asked a possible ordering, we should check each equation for certain value. If none of the iterations are true for the equality, we can say that the equality is wrong and if even one is correct we will say that the equality is correct.
Here selecting numbers to test the equality is the tricky part.
let's say that we have the numbers 2x,1/x and x^2 to compare. obviously the equality will change depending on the value of x. Observe each individual equality and make a decision. ( i assumed 1/2,0.9,1.5,3)
18 Aug 2025, 09:56
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This is very easily solvable using graphs. Create graphs of y = x^2, 2x and 1/x.
Graph of 1/x would be close to infinite at x = 0 and a smooth curve which goes to 0 as x goes to infinite. Make sure to intersect y = 1/x and x^2 at x = 1 and y = 1/x and 2x at x = 1/sqrt(2). Now you can see option 1 and 2 are correct from graphs directly.
Graph of 1/x would be close to infinite at x = 0 and a smooth curve which goes to 0 as x goes to infinite. Make sure to intersect y = 1/x and x^2 at x = 1 and y = 1/x and 2x at x = 1/sqrt(2). Now you can see option 1 and 2 are correct from graphs directly.
