Reasoning Aptitude
MATHEMATICAL OPERATIONS MCQs
Total Questions : 233
| Page 11 of 24 pages
Question 101. In the following questions, symbols #, $, @, * and © are used with the following meaning as illustrated below:'P#Q' means 'P is not smaller than Q'.'P$Q' means 'P is neither smaller than nor greater than Q'.'P@Q' means 'P is neither greater than nor equal to Q'.'P*Q' means 'P is not greater than Q'.'P©Q' means 'P is neither smaller than nor equal to Q'.Statements: J * D, Q # D, Q @ MConclusions: I. Q © J II. Q $ J
Answer: Option C. -> if either conclusion I or II is true.
J ≤ D -- (i); Q ≥ D -- (ii); Q < M -- (iii)combining (i) and (ii), we get:Q ≥ D ≥ J => Q > J (conclusion I) or Q = J (conclusion II).Hence, either conclusion I or conclusion II is true.
Question 102. In the following questions, symbols #, $, @, * and © are used with the following meaning as illustrated below:'P#Q' means 'P is not smaller than Q'.'P$Q' means 'P is neither smaller than nor greater than Q'.'P@Q' means 'P is neither greater than nor equal to Q'.'P*Q' means 'P is not greater than Q'.'P©Q' means 'P is neither smaller than nor equal to Q'.Statements: B $ K, K @ D, D # MConclusions: I. B $ M II. B @ M
Answer: Option D. -> if neither conclusion I nor II is true.
B = K -- (i); K < D -- (ii); D ≥ M -- (iii)From (i) and (ii), we get: D ≥ K = B -- (iv)from (iii) and (iv), no specific relation can be obtained between B and M. Therefore, B = M (conclusion I) and B < M (conclusion II) are not necessarily true.
Question 103. In the following questions, symbols #, $, @, * and © are used with the following meaning as illustrated below:'P#Q' means 'P is not smaller than Q'.'P$Q' means 'P is neither smaller than nor greater than Q'.'P@Q' means 'P is neither greater than nor equal to Q'.'P*Q' means 'P is not greater than Q'.'P©Q' means 'P is neither smaller than nor equal to Q'.Statements: F # G, N $ G, N © TConclusions: I. T © F II. N * F
Answer: Option B. -> if only conclusion II is true.
F ≥ G -- (i); N = G -- (ii); N > T -- (iii)combining all, we getF ≥ G = N > T => N ≤ F (conclusion II) and T > F.Hence, conclusion I (T > F) is not true but conclusion II is true.
Question 104. In the following questions, symbols #, $, @, * and © are used with the following meaning as illustrated below:'P#Q' means 'P is not smaller than Q'.'P$Q' means 'P is neither smaller than nor greater than Q'.'P@Q' means 'P is neither greater than nor equal to Q'.'P*Q' means 'P is not greater than Q'.'P©Q' means 'P is neither smaller than nor equal to Q'.Statements: H @ N, N © W, W # VConclusions: I. H @ V II. V @ N
Answer: Option B. -> if only conclusion II is true.
H < N -- (i); N > W -- (ii); W ≥ V -- (iii)From (ii) and (iii), we get N > W ≥ V --- (iv)From (i) and (iv), no specific relation can be obtained between H and V. Hence, H < V (conclusion I) is not necessarily true. But V < N (conclusion II) follows from equation (iv).
Question 105. In the following questions the symbols @, +, ©, $, ? and ? are used with the following meaning:'P?Q' means 'P is not equal to Q'.'P@Q' means 'P is greater than Q'.'P+Q' means 'P is smaller than Q'.'P©Q' means 'P is either greater than or equal to Q'.'P$Q' means 'P is either smaller than or equal to Q'.'P?Q' means 'P is equal to Q'.Now each of the following questions assuming the given statements to be true, find which of the two conclusions I and II given them is/are definitely true. Give answer.Statements: D @ B, B $ T, T + MConclusions: I. M @ B II. T © B
Answer: Option E. -> if both the conclusions I and II are true.
D > B -- (i); B ≤ T -- (ii); T < M -- (iii)Combining (ii) and (iii), we getM > T ≥ B => M > B (conclusion I) and T ≥ B (conclusion II).
Question 106. In the following given below, certain symbols are used with the following meanings:'P$Q' means 'P is neither equal to nor smaller than Q'.'P©Q' means 'P is not smaller than Q'.'P*Q' means 'P is neither greater nor smaller than Q'.'P#Q' means 'P is neither greater than nor equal to Q'.'P@Q' means 'P is not greater than Q'.Statements: M # K, K * D, D @ PConclusions: I. M @ P II. M * P
Answer: Option D. -> if neither conclusion I nor II is true.
M < K -- (i); K = D -- (ii); D ≤ P -- (iii)Combining all the equations, we get:P ≥ D = K > M => p > M. Hence, conclusion I (M ≤ P) and conclusion II (M = P) are not true.
Question 107. In the following given below, certain symbols are used with the following meanings:'P$Q' means 'P is neither equal to nor smaller than Q'.'P©Q' means 'P is not smaller than Q'.'P*Q' means 'P is neither greater nor smaller than Q'.'P#Q' means 'P is neither greater than nor equal to Q'.'P@Q' means 'P is not greater than Q'.Statements: H * D, D $ R, R © NConclusions: I. N * H II. N $ H
Answer: Option D. -> if neither conclusion I nor II is true.
H = D -- (i); D > R -- (ii); R ≥ N -- (iii)Combining (i) and (ii), we get:R > H = D -- (iv)From (iii) and (iv), we can't get any specific relation between N and H. Therefore, conclusion I (N = H) and conclusion II (N > H) are not true.
Question 108. In the following given below, certain symbols are used with the following meanings:'P$Q' means 'P is neither equal to nor smaller than Q'.'P©Q' means 'P is not smaller than Q'.'P*Q' means 'P is neither greater nor smaller than Q'.'P#Q' means 'P is neither greater than nor equal to Q'.'P@Q' means 'P is not greater than Q'.Statements: W © T, T $ M, B # MConclusions: I. W $ B II. M # W
Answer: Option E. -> if both the conclusions I and II are true.
W ≥ T -- (i); T > M -- (ii); B < M -- (iii)Combining all, we get W ≥ T > M > B=> W > B and W > M. Hence, both conclusions (W > B; M < W) are true.
Question 109. In the following given below, certain symbols are used with the following meanings:'P$Q' means 'P is neither equal to nor smaller than Q'.'P©Q' means 'P is not smaller than Q'.'P*Q' means 'P is neither greater nor smaller than Q'.'P#Q' means 'P is neither greater than nor equal to Q'.'P@Q' means 'P is not greater than Q'.Statements: Z @ R, R © D, D # TConclusions: I. D # Z II. Z # T
Answer: Option D. -> if neither conclusion I nor II is true.
Z ≤ R -- (i); R ≥ D -- (ii); D < T -- (iii)With these equations no relation can be established between D and Z, and Z and T.
Question 110. In the following questions, the symbols @, #, $, % and © are used with the following meaning as illustrated below:'P$Q' means 'P is not greater than Q'.'P@Q' means 'P is neither smaller than nor equal to Q'.'P%Q' means 'P is neither greater than not equal to Q'.'P©Q' means 'P is not smaller than Q'.'P#Q' means 'P is neither greater than nor smaller than Q'.Now in each of the following questions assuming the given statements to be true, find which of the three conclusions I, II and III given below them is are definitely true.Statements: M @ R, R © K, J % KConclusions: I. M @ J II. J % R III. K % M
Answer: Option E. -> All follow
M > R --- (i) R ≥ K --- (ii) J < K --- (iii)combining (i), (ii) and (iii), we get:M > R ≥ K > J => M > J (conclusion I),R > J (conclusion II),M > K (conclusion III),Hence, conclusion I (M > J), conclusion II (J < R) and conclusion III (K < M) are all true.
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