Inequality Posted by vuotaa.com Categories Blog Date 7 April 2024 Comments 0 comment Report a question What’s wrong with this question? You cannot submit an empty report. Please add some details. Inequality Inequality problems involve analyzing relationships between quantities or variables, typically expressed through mathematical symbols such as “<” (less than), “>” (greater than), “<=” (less than or equal to), or “>=” (greater than or equal to). Participants must determine the relative magnitudes of the quantities based on the given inequalities. This requires understanding arithmetic operations, number properties, and logical reasoning. Mastery of inequality problems enhances critical thinking, quantitative reasoning, and problem-solving skills. These problems are common in mathematics assessments, aptitude tests, and logical reasoning exercises, serving as a measure of one’s ability to interpret and manipulate mathematical expressions effectively. 1 / 50 1) Statement I ≥ N= T ≥ E > L ≥ G > M Conclusions I. G < N II. I ≥ L A) If either Conclusion I or II follows B) If only Conclusion II follows. C) If neither Conclusion I nor II follows. D) If only Conclusion I follows. State ment I ≥ N = T ≥ E > L ≥ G > M Conclusions I. G < N (True) II. I ≥ L (False) 2 / 50 2) Statements P > Q > M > N, Q = S Conclusions I. S > P II. N < S A) If either Conclusion I or II is true. B) If only Conclusion II is true. C) If neither Conclusion I nor II is true. D) If only Conclusion I is true. P > Q > M > N, Q = S ∴ P > S > M > N ∴ S > N (True) Hence, only Conclusion II is true. 3 / 50 3) Statement T ≥ I < G ≤ E = R < S Conclusions I. R > T II. S > I A) If both conclusions are true B) If only Conclusion II is true C) If neither Conclusion I nor II is true D) If only Conclusion I is true. Statement T≥ I < G ≤ E = R< S Conclusions I. R > T (False) II. S > I (True) Only Conclusion II is true. 4 / 50 4) Statement M < N = B ≤ V > C, L > K ≥ J = H ≥ B Conclusions I. N ≤ H II. B > J A) If only Conclusion I follows B) If either Conclusion I or II follows C) If only Conclusion II follows. D) If neither Conclusion I nor II follows. Statements M < N = B ≤ V > C Or M < N = B ≤ H = J ≤ K Con clu sions I. N ≤ H (True) II. B > J (False) Hence, only Conclusion I is definitely true 5 / 50 5) Which of the fol low ing ex pres sions will be true, if the given ex pres sion K ≥ G > H ≤ F is def i nitely true? A) F ≥ K B) K ≥ H C) H < K D) F < G Given, K ≥ G > H≤ F Now, we can check all the options one by one (a) F ≥ K (False) (b) H < K (True) (c) F < G (False) (d) K ≥ H (False) So, it is clear that option (b) is true. 6 / 50 6) Statement A ≥ B ≥ C = D > E ≤ F < G Conclusions I. E < B II. G > E A) If only Conclusion II follows B) If either Conclusion I or II follows. C) If only Conclusion I follows D) If both Conclusions I and II follow. Statement A ≥ B ≥ C = D > E ≤ F < G Conclusions I. E < B (True) II. G > E (True) 7 / 50 7) Statements Z < U ≤ D ≤ A ≤ M < S, Q > A ≤ Y < G Conclusions I. Z < Y II. S > Q A) If only Conclusion I is true B) If neither Conclusion I nor II is true C) If both Conclusions I and II are true D) If either Conclusion I or II is true. Statements Z < U ≤ D ≤ A ≤ M < S, Q > A ≤ Y < G ∴ Y ≥ A ≥ D ≥ U > Z and S > M ≥ A < Q Conclusions I. Z < Y (True) II. S > Q (False) ∴ Only Conclusion I is true. 8 / 50 8) Statement B > R ≥ A = N < D ≤ S Conclusions I. B > N II. S ≥ A A) If neither Conclusion I nor II is true B) If only Conclusion II is true C) If only Conclusion I is true. D) If both conclusions are true Statement B > R≥ A = N< D ≤ S Conclusions I. B > N (True) II. S ≥ A (False) Only Conclusion I is true. 9 / 50 9) State ment J>K ≥ H = U ≥ B ≤ T B II. H < R A) If neither Conclusion I nor II is true. B) If either Conclusion I or II is true C) If only Conclusion I is true D) If only Conclusion II is true Statement J > K ≥ H = U ≥ B ≤ T < F ≤ R Con clu sions I. J > B (True) II. H < R (False) ∴ Only Conclusion I is true. 10 / 50 10) State ment B ≤ C = X ≥ Y < Z Conclusions I. B > Z II. B = Z A) If only Conclusion I is true. B) If only Conclusion II is true C) If both Conclusions are true. D) If either Conclusion I or II is true. State ment B ≤ C = X ≥ Y < Z Conclusions I. B > Z (False) II. B = Z (False) So, neither Conclusion I nor II follows. 11 / 50 11) Statement P = L > O ≥ K > U > M, N < H ≤ M = B < K Conclusions I. L > B II. N < U A) If only Conclusion I follows B) If only Conclusion II follows. C) If both Conclusions I and II follow. D) If either Conclusion I or II follows Statement P = L > O ≥ K > U > M Or P = L > O ≥ K > U > M ≥ H > N Or L > O ≥ K > U > M = B < K Con clu sions I. L > B (True) II. N < U (True) Hence, both the conclusions are definitely true. 12 / 50 12) State ments V > B ≥ G = H > F < D ≤ T, Q < W = E ≤ F Conclusions. I. B > W II. E ≥ B A) If only Conclusion I follows B) If only Conclusion II follows. C) If neither Conclusion I nor II follows. D) If either Conclusion I or II follows. State ments V > B ≥ G = H > F < D ≤ T Or V > B ≥ G = H > F ≥ E = W > Q Conclusions I. B > W (True) II. E ≥ B (False) Hence, only Conclusions I is definitely true 13 / 50 13) State ments M < N = B ≤ V > C, L > K ≥ J = H ≥ B Conclusions I. N ≤ H II. B > J A) If either Conclusion I or II follows. B) If only Conclusion II follows. C) If only Conclusion I follows D) If neither Conclusion I nor II follows. Statements M < N = B ≤ V > C Or M < N = B ≤ H = J ≤ K Conclusions I. N ≤ H (True) II. B > J (False) Hence, only Conclusion I is definitely true 14 / 50 14) Statements P ≤ R < T = U, Q ≥ T ≤ S ≥ V Conclusions I. Q > P II. V < R A) If only Conclusion I follows B) If only Conclusion II follows C) If neither Conclusion I nor II follow D) If either Conclusion I or II follows. State ments P ≤ R < T = U, Q ≥ T ≤ S ≥ V ∴ Q ≥ T > R ≥ P and R < T ≤ S ≥ V Conclusions I. Q > P (True) II. V < R (False) 15 / 50 15) Statement P< R ≤ A ≤ I > S ≥ E Conclusions I. P < I II. E ≤ A A) If only Conclusion I is true. B) If both conclusions are true C) If neither Conclusion I nor II is true D) If only Conclusion II is true Statement P S> E Conclusions I. P < I (True) II. E ≤ A (False) Only Conclusion I is true 16 / 50 16) Statement W > A = S ≥ H < I ≤ N ≤ G Conclusions I. H < W II. G > H A) If either Conclusion I or II follows B) If both Conclusions I and II follow C) If only Conclusion I follows. D) If only Conclusion II follows. State ment W > A = S ≥ H < I ≤ N ≤ G Conclusions I. H < W (True) II. G > H (True) 17 / 50 17) Statements L ≤ T ≤ I ≥ M < X, W < P ≤ L ≥ B ≥ K Conclusions I. K < X II. W > M A) If only Conclusion II is true B) If neither Conclusion I nor II is true C) If either Conclusion I or II is true D) If only Conclusion I is true Statements L ≤ T ≤ I ≥ M < X, W < P ≤ L ≥ B ≥ K ∴ X > M ≤ I ≥ T ≥ L ≥ B ≥ K and W < P ≤ L ≤ I ≥ M Conclusions I. K < X (False) II. W > M (False) ∴ Neither Conclusion I nor II is true 18 / 50 18) Which of the following should be placed in the blank spaces respectively (in the same order from left to right in order to complete the given expression in such a manner that both S > P as well as A ≤ E definitely hold true? S _ H _ A _ P _ E A) >, ≥, <, ≤ B) >, >, ≥ , = C) ≥, >, = , ≤ D) >, ≥ , <, < Taking option (a), we have S ≥ H > A = P ≤ E ∴ S > P (true) and A ≤ E (true) 19 / 50 19) Statements A > B > C < D, C = E > G Conclusions I. D > E II. B > E A) If only Conclusion II is true. B) If either Conclusion I or II is true. C) If only Conclusion I is true. D) If both Conclusions are true. A > B > C < D, C = E > G ∴ A > B > C, C = E, C < D ∴ A > B > E = C < D ∴ B > E (True) D > E (True) Hence, both Conclusions are true. 20 / 50 20) Statement S ≤ T = E ≤ P = N ≤ G Conclusions I. G > S II. G = S A) If both conclusions are true B) If only Conclusion I is true. C) If only Conclusion II is true D) If neither Conclusion I nor II is true Statement S≤ T = E ≤ P = N≤ G Conclusions I. G > S (False) II. G = S (False) Hence, neither Conclusion I nor II is true 21 / 50 21) State ments Z < U ≤ D ≤ A ≤ M < S, Q > A ≤ Y < G Conclusions I. M ≥ U II. G > Z A) If only Conclusion I is true B) If neither Conclusion I nor II is true C) If both Conclusions I and II are true. D) If only Conclusion II is true. State ments Z < U ≤ D ≤ A ≤ M < S, Q > A ≤ Y < G ∴ U ≤ D ≤ A ≤ M and G > Y ≥ A ≥ D ≥ U > Z Conclusions I. M ≥ U (True) II. G > Z (True) 22 / 50 22) Statement T < U = V < S > P > Q Conclusions I. S > T II. V < Q A) If only Conclusion I is true. B) If only Conclusion II is true. C) If neither Conclusion I nor II is true. D) If either Conclusion I or II is true. T < U = V < S > P > Q ∴ T < U = V < S ∴ T < S ⇒ S > T (True) and V < Q (False) Hence, only Conclusion I follows. 23 / 50 23) Statements V > B ≥ G = H > F < D ≤ T, Q < W = E ≤ F Conclusions I. B > W II. E ≥ B A) If either Conclusion I or II follows B) If only Conclusion II follows. C) If only Conclusion I follows D) If neither Conclusion I nor II follows. Statements V > B ≥ G = H > F < D ≤ T Or V > B ≥ G = H > F ≥ E = W > Q Con clu sions I. B > W (True) II. E ≥ B (False) Hence, only Conclusion I is definitely true 24 / 50 24) Statement C < O ≤ D = S > A ≥ P ≥ Q Conclusions I. Q < D II. C < A A) If only Conclusion I follows. B) If neither Conclusion I nor II follows. C) If either Conclusion I or II follows D) If only Conclusion II follows. State ment C < O ≤ D = S > A ≥ P ≥ Q Conclusions I. Q < D (True) II. C < A (False) 25 / 50 25) Statements X ≥ G > H ≥ I, M > H ≥ L Conclusions I. X > M II. X > L A) If either Conclusion I or II follows. B) If only Conclusion II follows. C) If only Conclusion I follows. D) If neither Conclusion I nor II follows. Statements X ≥ G > H ≥ I, M > H ≥ L ∴ X ≥ G > H < M and X ≥ G > H > L Conclusions I. X > M (False) II. X > L (True) Hence only conclusion II is true. 26 / 50 26) State ments L ≤ T ≤ I ≥ M < X, W < P ≤ L ≥ B ≥ K Con clu sions I. K ≥ M II. P > M A) If either Conclusion I or II is true. B) If only Conclusion II is true C) If only Conclusion I is true D) If neither Conclusion I nor II is true. Statements L ≤ T ≤ I ≥ M < X, W < P ≤ L ≥ B ≥ K ∴ K ≤ B ≤ L ≤ T ≤ I ≥ M and P ≤ L ≤ T ≤ I ≥ M Conclusions I. K ≥ M (False)II. P > M (False)∴ Neither Conclusion I nor II follows. 27 / 50 27) Statement G ≤ I = A ≤ N < T Conclusions I. G < T II. G = T A) If both Conclusions are true. B) If either Conclusion I or II is true. C) If only Conclusion I is true. D) If only Conclusion II is true State ment G ≤ I = A ≤ N < T Conclusions I. G < T (True) II. G = T (False) 28 / 50 28) Statements G ≥ H = I < J, J > K, G < L Conclusions I. K < H II. L > I A) If only Conclusion II follows B) If either Conclusion I or II follows C) If both conclusions follow D) If neither Conclusion I nor II follows. On combining statements, L > G ≥ H = I < J > K Conclusions I. K < H (False) II. L > I (True) So, only Conclusion II follows. 29 / 50 29) Statements C ≥ D = E, A = B ≤ S ≥ C Conclusions I. C < A II. D ≤ B A) If either Conclusion I or II follows. B) If only Conclusion II follows. C) If only Conclusion I follows. D) If neither Conclusion I nor II follows. State ments C ≥ D = E, A = B ≤ S ≥ C ∴ A = B ≤ S ≥ C ≥ D = E Conclusions I. C < A (may be true) II. D ≤ B (may be true) Hence, neither Conclusion I nor II is true. 30 / 50 30) State ments Z < U ≤ D ≤ A ≤ M < S, Q > A ≤ Y < G Con clu sions I. Z < Y II. S > Q A) If only Conclusion I is true. B) If both Conclusions I and II are true C) If either Conclusion I or II is true D) If neither Conclusion I nor II is true State ments Z < U ≤ D ≤ A ≤ M < S, Q > A ≤ Y < G ∴ Y ≥ A ≥ D ≥ U > Z and S > M ≥ A < Q Conclusions I. Z < Y (True) II. S > Q (False) ∴ Only Conclusion I follows. 31 / 50 31) Statements M < N > R > W, E = J > L > W Conclusions I. E > W II. M > L A) If only Conclusion I is true. B) If neither Conclusion I nor II is true. C) If either Conclusion I or II is true. D) If only Conclusion II is true. M < N > R > W and E = J > L > W ∴ E > W Hence, only Conclusion I is true. 32 / 50 32) In which of the fol low ing ex pres sions the ex pres sion ‘M > R’ does not hold true? A) M = P < Q = R B) R = P < Q < M C) M > P ≥ Q = R D) M = P > Q > R We can check all the options one by one. From option (a), M = P> Q > R ⇒M> R So, expression M > R holds true for option (a). From option (b), M> P≥ Q = R ⇒M< R So, expression M> R holds true for option (b). From option (c), R = P< Q < M ⇒M> R So, expression M> R holds true for option (c). From option (d), M = P< Q = R ⇒M< R So, expression M> R does not hold true for option (d). 33 / 50 33) State ments A > B = R ≥ S ≥ T, X < J ≤ K < T Conclusions I. A > X II. R ≥ T A) If both Conclusions I and II follow. B) If only Conclusion II follows. C) If only Conclusion I follows. D) If either Conclusion I or II follows. State ments A > B = R ≥ S ≥ T, X < J ≤ K < T ∴ A > B = R ≥ S ≥ T > K ≥ J > X Conclusions I. A > X (True) II. R ≥ T (True) Hence, both I and II are true. 34 / 50 34) State ment G ≤ H ≤ R ≥ S = T > U Conclusions I. R ≥ G II. H > U A) If only Conclusion I is true. B) If either Conclusion I or II is true. C) If only Conclusion II is true D) If both Conclusions are true. State ment G ≤ H ≤ R ≥ S = T > U Conclusions I. R ≥ G (True) II. H > U (False) So, only Conclusion I follows. 35 / 50 35) Statements P = L > O ≥ K > U > M, N < H ≤ M = B < K Conclusions I. L > B II. N < U A) If only Conclusion II follows. B) If only Conclusion I follows C) If both Conclusions I and II follows. D) If either Conclusion I or II follows. Statements P = L > O ≥ K > U > M Or P = L > O ≥ K > U > M ≥ H > N Or L > O ≥ K > U > M = B < K Conclusions I. L > B (True) II. N < U (True) Hence, both Conclusions are definitely true. 36 / 50 36) Statements X ≥ G = H, G > J ≥ L, J ≥ K < Y Conclusions I. X > L II. K < G A) If only Conclusion I follows. B) If only Conclusion II follows. C) If both Conclusions I and II follow. D) If either Conclusion I or II follows. State ments X ≥ G = H, G > J ≥ L, J ≥ K < Y ∴ X ≥ G = H > J ≥ L and G = H > J ≥ K < Y Conclusions I. X > L (True) II. K < G (True) Hence, both I and II are true. 37 / 50 37) Statement Y < J = P ≥ R > I Conclusions I. J > I II. Y < R A) If either Conclusion I or II follows B) If only Conclusion II follows C) If only Conclusion I follows. D) If neither Conclusion I nor II follows. Statement Y < J = P ≥ R > I Conclusions I. J > I (True) II. Y < R (False) So, only Conclusion I follows. 38 / 50 38) State ment C ≤ L = E ≤ R ≤ K = P ≥ O Conclusions I. P = C II. C < P A) If neither Conclusion I nor II follows. B) If either Conclusion I or II follows C) If only Conclusion II follows. D) If only Conclusion I follows. State ment C ≤ L = E ≤ R ≤ K = P ≥ O Conclusions I. P = C (May be true) II. C < P (May be true) 39 / 50 39) State ments J > K ≥ H = U ≥ B ≤ T < F ≤ R Conclusions I. J > B II. H < R A) If neither Conclusion I nor II is true B) If either Conclusion I or II is true. C) If only Conclusion I is true. D) If only Conclusion II is true. Statement J > K ≥ H = U ≥ B ≤ T < F ≤ R Conclusions I. J > B (True) II. H < R (False) 40 / 50 40) If M > N ≤ O < P and T < O > C ≥ Z are true, then which of the following options is definitely true? A) M > O B) T < P C) O = Z D) C = T Given, M > N ≤ O < P, T < O > C ≥ Z ∴ P > O > T and N ≤ O > C ≥ Z (a) M > O (false) (b) C = T (false) (c) O = Z (false) (d) T < P (true) (e) N ≥ Z (false) ∴ Only option (d) is true 41 / 50 41) Statements U > B ≥ M ≤ G;L < Y ≤ M Conclusions I. U > L II. G ≤ L A) If neither Conclusion I nor II is true B) If only Conclusion I is true. C) If both conclusions are true D) If only Conclusion II is true Statements U >B ≥ M≤ G; L < Y ≤ M ∴ U > B ≥ M ≥ Y > L; G ≥ M ≥ Y > L Conclusions I. U > L (True) II. G ≤ L (False) Only Conclusion I is true. 42 / 50 42) Statement S > M = Z > T < Q > V Conclusions I. V = S II. Q > M A) If either Conclusion I or II is true. B) If neither Conclusion I nor II is true. C) If only Conclusion I is true. D) If only Conclusion II is true. S > M = Z > T < Q > V ∴ M < S > T < Q > V Hence, neither Conclusion I nor II is true. 43 / 50 43) Statements V ≥ K > M = N, M > 5, T < K Conclusions I. T < N II. V = 5 A) If both conclusions follow B) If only Conclusion II follows C) If neither Conclusion I nor II follows. D) If either Conclusion I or II follows On combining statements, V ≥ K > M = N > 5, T < K Conclusions I. T < N (False) II. V = 5 (False) So, neither Conclusion I nor II follows. 44 / 50 44) Statements M > L ≥ K ≤ J, N ≥ R ≥ S = M Conclusions I. R > J II. J ≥ R A) If neither Conclusion I nor II follows. B) If only Conclusion II follows. C) If either Conclusion I or II follows. D) If only Conclusion I follows. Statements M > L ≥ K ≤ J, N ≥ R ≥ S = M ∴ N ≥ R ≥ S = M > L ≥ K ≤ J Conclusions I. R > J (False) II. J ≥ R (False) Hence, Neither Conclusion I Nor II is true. 45 / 50 45) State ments Z < U ≤ D ≤ A ≤ M < S, Q > A ≤ Y < G Con clu sions I. M ≥ U II. G > Z A) If both Conclusions I and II are true B) If neither Conclusion I nor II is true C) If only Conclusion II is true D) If only Conclusion I is true. State ments Z < U ≤ D ≤ A ≤ M < S, Q > A ≤ Y < G ∴ U ≤ D ≤ A ≤ M and G > Y≥ A ≥ D ≥ U > Z Con clu sions I. M ≥ U (True) II. G > Z (True) ∴ Both Conclusions I and II are true 46 / 50 46) Statements Q ≥ U > I < C = K > L, G < L, C < H Conclusions I. I < L II. C > G A) If both conclusions follow. B) If only Conclusion I follows. C) If none follows D) If only Conclusion II follows. State ments Q ≥ U > I < C = K > L> G, C < H Conclusions I. I < L (False) II. C > G (True) 47 / 50 47) Statements L > M = O ≥ P, N ≤ M ≥ S ≥ T Conclusions I. T ≤ P II. N < L A) If either Conclusion I or II follows. B) If only Conclusion I follows C) If neither Conclusion I nor II follow D) If only Conclusion II follows State ments L > M = O ≥ P, N ≤ M ≥ S ≥ T ∴ T ≤ S ≤ M = O ≥ P and N ≤ M < L Conclusions I. T ≤ P (False) II. N < L (True) 48 / 50 48) State ments L ≤ T ≤ I ≥ M < X, W < P ≤ L ≥ B ≥ K Con clu sions I. K < X II. W > M A) If only Conclusion II is true. B) If only Conclusion I is true C) If either Conclusion I or II is true. D) If neither Conclusion I nor II is true State ments L ≤ T ≤ I ≥ M < X, W < P ≤ L ≥ B ≥ K ∴ X > M ≤ I ≥ T ≥ L ≥ B ≥ K and W < P ≤ L ≤ I ≥ M Con clu sions I. K < X (False) II. W > M (False) ∴ Neither Conclusion I nor II follows. 49 / 50 49) Statement F ≤ B = I ≤ C = A ≥ S > E Conclusions I. S ≥ B II. F > E A) If neither Conclusion I nor II follows. B) If only Conclusion I follows. C) If either Conclusion I or II follows D) If only Conclusion II follows. State ment F ≤ B = I ≤ C = A ≥ S > E Conclusions I. S ≥ B (False) II. F > E (False) 50 / 50 50) State ments L ≤ T ≤ I ≥ M < X, W < P ≤ L ≥ B ≥ K Conclusions I. K ≥ M II. P > M A) If either Conclusion I or II is true B) If neither Conclusion I nor II is true C) If only Conclusion I is true D) If only Conclusion II is true. State ments L ≤ T ≥ I ≥ M < X, W < P ≤ L ≥ B ≥ K ∴ K ≤ B ≤ L ≤ T ≤ I ≥ M and P ≤ L ≤ T ≤ I ≥ M Conclusions I. K ≥ M (False) II. P > M (False) Your score is LinkedIn Facebook Twitter 0% Exit Share: vuotaa.com Previous post Problems Based on Ages 7 April 2024 Next post Data Sufficiency 7 April 2024 You may also like Sentence Completion 7 April, 2024 Passage and Conclusions 7 April, 2024 Cause and Effects 7 April, 2024
