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 T ≥ I < G ≤ E = R < S Conclusions I. R > T II. S > I A) If neither Conclusion I nor II is true B) If only Conclusion II is true C) If both conclusions are 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. 2 / 50 2) Statement S > M = Z > T < Q > V Conclusions I. V = S II. Q > M A) If only Conclusion I is true. B) If only Conclusion II is true. C) If either Conclusion I or II is true. D) If neither Conclusion I nor II is true. S > M = Z > T < Q > V ∴ M < S > T < Q > V Hence, neither Conclusion I nor II is true. 3 / 50 3) State ment G ≤ H ≤ R ≥ S = T > U Conclusions I. R ≥ G II. H > U A) If both Conclusions are true. B) If only Conclusion II is true C) If either Conclusion I or II is true. D) If only Conclusion I is true. State ment G ≤ H ≤ R ≥ S = T > U Conclusions I. R ≥ G (True) II. H > U (False) So, only Conclusion I follows. 4 / 50 4) Statements Q ≥ U > I < C = K > L, G < L, C < H Conclusions I. I < L II. C > G A) If only Conclusion I follows. B) If only Conclusion II follows. C) If both conclusions follow. D) If none follows State ments Q ≥ U > I < C = K > L> G, C < H Conclusions I. I < L (False) II. C > G (True) 5 / 50 5) State ments L ≤ T ≤ I ≥ M < X, W < P ≤ L ≥ B ≥ K Conclusions I. K ≥ M II. P > M 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. 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) 6 / 50 6) Statements M < N > R > W, E = J > L > W Conclusions I. E > W II. M > L A) If neither Conclusion I nor II is true. B) If only Conclusion I is true. C) If only Conclusion II is true. D) If either Conclusion I or II is true. M < N > R > W and E = J > L > W ∴ E > W Hence, only Conclusion I is true. 7 / 50 7) Statements X ≥ G = H, G > J ≥ L, J ≥ K < Y Conclusions I. X > L II. K < G A) If both Conclusions I and II follow. B) If either Conclusion I or II follows. C) If only Conclusion II follows. D) If only Conclusion I 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. 8 / 50 8) Statements P > Q > M > N, Q = S Conclusions I. S > P II. N < S A) If only Conclusion I is true. B) If neither Conclusion I nor II is true. C) If only Conclusion II is true. D) If either Conclusion I or II is true. P > Q > M > N, Q = S ∴ P > S > M > N ∴ S > N (True) Hence, only Conclusion II is true. 9 / 50 9) Statement S ≤ T = E ≤ P = N ≤ G Conclusions I. G > S II. G = S 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 Statement S≤ T = E ≤ P = N≤ G Conclusions I. G > S (False) II. G = S (False) Hence, neither Conclusion I nor II is true 10 / 50 10) Statements V ≥ K > M = N, M > 5, T < K Conclusions I. T < N II. V = 5 A) If only Conclusion II follows B) If both conclusions follow C) If either Conclusion I or II follows D) If neither Conclusion I nor 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. 11 / 50 11) 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 neither Conclusion I nor II follows. D) If only Conclusion I follows. Statement Y < J = P ≥ R > I Conclusions I. J > I (True) II. Y < R (False) So, only Conclusion I follows. 12 / 50 12) 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) 13 / 50 13) State ments L ≤ T ≤ I ≥ M < X, W < P ≤ L ≥ B ≥ K Con clu sions I. K ≥ M II. P > M A) If only Conclusion II is true B) If either Conclusion I or II is true. C) If neither Conclusion I nor II is true. D) If only Conclusion I 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. 14 / 50 14) Statements L ≤ T ≤ I ≥ M < X, W < P ≤ L ≥ B ≥ K Conclusions I. K < X II. W > M A) If only Conclusion I is true B) If only Conclusion II is true C) If either Conclusion I or II is true D) If neither Conclusion I nor II 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 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) In which of the fol low ing ex pres sions the ex pres sion ‘M > R’ does not hold true? A) R = P < Q < M B) M = P > Q > R 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). 17 / 50 17) Statements V > B ≥ G = H > F < D ≤ T, Q < W = E ≤ F Conclusions I. B > W II. E ≥ B A) If neither Conclusion I nor II follows. B) If only Conclusion II follows. C) If only Conclusion I follows D) If either Conclusion I or 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 18 / 50 18) Statements A > B > C < D, C = E > G Conclusions I. D > E II. B > E 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. 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. 19 / 50 19) Statements L > M = O ≥ P, N ≤ M ≥ S ≥ T Conclusions I. T ≤ P II. N < L 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 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) 20 / 50 20) Statement C < O ≤ D = S > A ≥ P ≥ Q Conclusions I. Q < D II. C < A 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 ment C < O ≤ D = S > A ≥ P ≥ Q Conclusions I. Q < D (True) II. C < A (False) 21 / 50 21) State ment C ≤ L = E ≤ R ≤ K = P ≥ O Conclusions I. P = C II. C < P A) If only Conclusion II follows. B) If neither Conclusion I nor II follows. C) If either Conclusion I or 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) 22 / 50 22) 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 neither Conclusion I nor II is true C) If either Conclusion I or II is true D) If both Conclusions I and II are 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. 23 / 50 23) If M > N ≤ O < P and T < O > C ≥ Z are true, then which of the following options is definitely true? A) O = Z B) T < P C) M > O 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 24 / 50 24) 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. 25 / 50 25) Statements C ≥ D = E, A = B ≤ S ≥ C Conclusions I. C < A II. D ≤ 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 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. 26 / 50 26) State ments A > B = R ≥ S ≥ T, X < J ≤ K < T Conclusions I. A > X II. R ≥ T A) If either Conclusion I or II follows. B) If only Conclusion I follows. C) If only Conclusion II follows. D) If both Conclusions I and II follow. 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. 27 / 50 27) 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) H < K C) F < G D) K ≥ H 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. 28 / 50 28) Statements U > B ≥ M ≤ G;L < Y ≤ M Conclusions I. U > L II. G ≤ L A) If only Conclusion II is true B) If only Conclusion I is true. C) If neither Conclusion I nor II is true D) If both conclusions are 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. 29 / 50 29) State ment B ≤ C = X ≥ Y < Z Conclusions I. B > Z II. B = Z 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 B ≤ C = X ≥ Y < Z Conclusions I. B > Z (False) II. B = Z (False) So, neither Conclusion I nor II follows. 30 / 50 30) Statement P = L > O ≥ K > U > M, N < H ≤ M = B < K Conclusions I. L > B II. N < U 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 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. 31 / 50 31) 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 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 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. 32 / 50 32) Statements P = L > O ≥ K > U > M, N < H ≤ M = B < K Conclusions I. L > B II. N < U A) If either Conclusion I or II follows. B) If both Conclusions I and II follows. C) If only Conclusion I follows D) If only Conclusion 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. 33 / 50 33) Statements X ≥ G > H ≥ I, M > H ≥ L Conclusions I. X > M II. X > L A) If only Conclusion II follows. B) If either Conclusion I or II follows. C) If neither Conclusion I nor II follows. D) If only Conclusion I 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. 34 / 50 34) State ment J>K ≥ H = U ≥ B ≤ T B II. H < R 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 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. 35 / 50 35) Statement T < U = V < S > P > Q Conclusions I. S > T II. V < Q 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 neither Conclusion I nor 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. 36 / 50 36) 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 I follows. C) If neither Conclusion I nor II follows. D) If only Conclusion II follows. State ment I ≥ N = T ≥ E > L ≥ G > M Conclusions I. G < N (True) II. I ≥ L (False) 37 / 50 37) State ments Z < U ≤ D ≤ A ≤ M < S, Q > A ≤ Y < G Con clu sions I. M ≥ U II. G > Z A) If only Conclusion II is true B) If only Conclusion I is true. C) If both Conclusions I and II are true D) If neither Conclusion I nor 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 Con clu sions I. M ≥ U (True) II. G > Z (True) ∴ Both Conclusions I and II are true 38 / 50 38) 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 II is true. D) If only Conclusion I is true. Statement J > K ≥ H = U ≥ B ≤ T < F ≤ R Conclusions I. J > B (True) II. H < R (False) 39 / 50 39) 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 I is true. C) If only Conclusion II 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. 40 / 50 40) Statement G ≤ I = A ≤ N < T Conclusions I. G < T II. G = T A) If only Conclusion II is true B) If both Conclusions are true. C) If either Conclusion I or II is true. D) If only Conclusion I is true. State ment G ≤ I = A ≤ N < T Conclusions I. G < T (True) II. G = T (False) 41 / 50 41) Statement M < N = B ≤ V > C, L > K ≥ J = H ≥ B Conclusions I. N ≤ H II. B > J A) If only Conclusion II follows. B) If either Conclusion I or II follows C) If neither Conclusion I nor II follows. D) If only Conclusion I 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 42 / 50 42) Statements P ≤ R < T = U, Q ≥ T ≤ S ≥ V Conclusions I. Q > P II. V < R A) If neither Conclusion I nor II follow B) If only Conclusion II follows C) If only Conclusion I follows 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) 43 / 50 43) 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 either Conclusion I or II follows. C) If only Conclusion 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. 44 / 50 44) Statement F ≤ B = I ≤ C = A ≥ S > E Conclusions I. S ≥ B II. F > E A) If only Conclusion I follows. B) If only Conclusion II follows. C) If either Conclusion I or II follows D) If neither Conclusion I nor II follows. State ment F ≤ B = I ≤ C = A ≥ S > E Conclusions I. S ≥ B (False) II. F > E (False) 45 / 50 45) State ments Z < U ≤ D ≤ A ≤ M < S, Q > A ≤ Y < G Conclusions I. M ≥ U II. G > Z A) If only Conclusion II is true. B) If both Conclusions I and II are true. C) If neither Conclusion I nor 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 Conclusions I. M ≥ U (True) II. G > Z (True) 46 / 50 46) 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 neither Conclusion I nor II follows. C) If only Conclusion I follows D) If only Conclusion 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 47 / 50 47) 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 either Conclusion I or II follows. D) If neither Conclusion I nor 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 48 / 50 48) Statement A ≥ B ≥ C = D > E ≤ F < G Conclusions I. E < B II. G > E A) If only Conclusion I follows B) If both Conclusions I and II follow. C) If either Conclusion I or II follows. D) If only Conclusion II follows Statement A ≥ B ≥ C = D > E ≤ F < G Conclusions I. E < B (True) II. G > E (True) 49 / 50 49) Statement W > A = S ≥ H < I ≤ N ≤ G Conclusions I. H < W II. G > H A) If only Conclusion II follows. B) If only Conclusion I follows. C) If either Conclusion I or II follows D) If both Conclusions I and II follow State ment W > A = S ≥ H < I ≤ N ≤ G Conclusions I. H < W (True) II. G > H (True) 50 / 50 50) 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 neither Conclusion I nor II is true D) If either Conclusion I or 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. 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
