If a/b<c/d & bd < 0, which of the following inequalities must be true?

I did like this, suppose if we take a/d = 1/-4 means a=1, b=-4 and c/d = 1/2
then therefore bd< 0 -4x2 =-8 and a/b<c/d also
solving the options will give only 3rd one correct

Bunuel can you how to solve this with assuming numbers

"MUST BE TRUE" ("ALWAYS TRUE"/"IS TRUE") questions:


"COULD BE TRUE" questions:

Alright, listen up - let me give you the real deal on picking numbers for this tricky problem.

The Brutal Truth About Number Selection
Look, I'm gonna be straight with you: picking numbers for inequality problems can be a real headache. But sometimes it's the only way your brain will actually get what's happening, so let's talk strategy.
My "Don't Overthink It" Number Selection Rules

Rule #1: Keep It Simple, Smart Cookie

• Use integers whenever possible (1, 2, -1, -3, etc.)
• Avoid fractions like 7/13 unless you enjoy unnecessary suffering
• Make denominators like 1, 2, or -1 so the math doesn't make you cry

Rule #2: Remember What You're Trying to Prove We need bd < 0, which means b and d have opposite signs. So:

• Case 1: b positive, d negative
• Case 2: b negative, d positive

Rule #3: Work Backwards From What You Need Here's the systematic approach (because I'm obsessed with systems):

1. Pick your b and d first - they need opposite signs
2. Calculate what a/b and c/d need to look like for a/b < c/d
3. Choose a and c to make that inequality work
4. Crunch those numbers

Example Walkthrough (Because I'm Really Verbose)

Let's say I pick b = 2, d = -1 (opposite signs ✓)
Now I need a/b < c/d, which becomes a/2 < c/(-1) = -c
So I need a/2 < -c, or a < -2c
If I make c = 1, then I need a < -2. So let's use a = -3.
Check: a/b = -3/2 = -1.5, c/d = 1/(-1) = -1 Is -1.5 < -1? Yes! (More negative = smaller)
The calculation: ad - bc = (-3)(-1) - (2)(1) = 3 - 2 = 1 > 0

The Real Talk: Should You Actually Do This?

Absolutely not as your primary strategy. Here's why:

1. It's time-consuming - The GMAT doesn't give you all day
2. You might pick bad examples - I've seen students accidentally choose numbers that don't even satisfy the original conditions (I'm looking at you, past me)
3. The algebra is actually faster once you get comfortable with it

When Number-Picking IS Worth It:

• When you're totally lost and need to see a pattern
• For double-checking your algebraic work
• When the algebra is getting messy and you want a sanity check

Bottom Line Strategy:

1. Learn the algebra first (cross-multiply, watch for sign flips when bd < 0)
2. Use numbers to verify if you have time
3. Don't beat yourself up if the number approach feels clunky - it's supposed to be the backup plan, not the main event

The test writers know that picking numbers can work, so they design these problems to be solvable but not necessarily easy with numbers. That's not your fault - that's just them being their usual charming selves.

You got this. Now go practice the algebraic approach and save the numbers for when you really need them.