Inequalities

Inequality questions chain comparisons like A > B ≥ C. A conclusion is definitely true only if one unbroken chain of signs, all pointing the same way, connects the two letters.

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Tap an answer. You'll see if it's right, and why. Easy ones come first.

1. Q1Hard

   If Q > R < T > S ≥ L > U, which is definitely true?

   1. AU ≥ T
   2. BL < T
   3. CR = U
   4. DR < S
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   Answer: B. L < T

   💡 Follow the chain Q > R < T > S ≥ L > U between the two letters: only "L < T" holds whatever the values.

2. Q2Hard

   If V > S > K ≤ R = T ≥ P, which is definitely true?

   1. AS ≤ R
   2. BP ≤ R
   3. CS = R
   4. DV < T
   Show answer

   Answer: B. P ≤ R

   💡 Follow the chain V > S > K ≤ R = T ≥ P between the two letters: only "P ≤ R" holds whatever the values.

3. Q3Hard

   If L = J < T = U ≥ V > P, which is definitely true?

   1. AT ≤ P
   2. BT > L
   3. CL ≥ T
   4. DV = T
   Show answer

   Answer: B. T > L

   💡 Follow the chain L = J < T = U ≥ V > P between the two letters: only "T > L" holds whatever the values.

4. Q4Hard

   If P > M > W ≤ U ≤ S ≤ V, which is definitely true?

   1. AU ≥ M
   2. BW ≤ V
   3. CP ≥ U
   4. DP < U
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   Answer: B. W ≤ V

   💡 Follow the chain P > M > W ≤ U ≤ S ≤ V between the two letters: only "W ≤ V" holds whatever the values.

5. Q5Hard

   If M < T < V ≤ U > J ≥ R, which is definitely true?

   1. AR > V
   2. BU > R
   3. CM < R
   4. DM = V
   Show answer

   Answer: B. U > R

   💡 Follow the chain M < T < V ≤ U > J ≥ R between the two letters: only "U > R" holds whatever the values.

6. Q6Hard

   If K ≤ V = P < U ≤ J ≤ R, which is definitely true?

   1. AR ≥ P
   2. BK ≥ U
   3. CK > U
   4. DU ≥ R
   Show answer

   Answer: A. R ≥ P

   💡 Follow the chain K ≤ V = P < U ≤ J ≤ R between the two letters: only "R ≥ P" holds whatever the values.

7. Q7Hard

   If R > S < W ≤ M ≤ J ≥ V, which is definitely true?

   1. AJ > S
   2. BR > J
   3. CM = V
   4. DV ≤ R
   Show answer

   Answer: A. J > S

   💡 Follow the chain R > S < W ≤ M ≤ J ≥ V between the two letters: only "J > S" holds whatever the values.

8. Q8Hard

   If T ≤ R < P < M = V = W, which is definitely true?

   1. AW > T
   2. BT > M
   3. CW ≤ P
   4. DR ≥ W
   Show answer

   Answer: A. W > T

   💡 Follow the chain T ≤ R < P < M = V = W between the two letters: only "W > T" holds whatever the values.