Reasoning Aptitude
MATHEMATICAL OPERATIONS MCQs
Total Questions : 233
| Page 18 of 24 pages
Question 171. In the following questions, the symbols, @, #, $, * and % are used as illustrated below:'P@Q' means 'P is not smaller than Q'.'P#Q' means 'P is neither greater than nor equal to Q'.'P$Q' means 'P is neither smaller than nor greater than Q'.'P*Q' means 'P is not greater than Q'.'P%Q' means 'P is not greater than Q'.Statements: F * M, M % R, E @ FConclusions: I. M % E II. R @ E
Answer: Option D. -> if neither conclusion I nor II is true.
F ≤ M -- (i); M > R -- (ii); E ≥ F -- (iii)From (I) and (ii), no specific relation can be obtained between M and E. Similarly, no specific relation can be obtained between R and E.
Question 172. In the following questions, the symbols, @, #, $, * and % are used as illustrated below:'P@Q' means 'P is not smaller than Q'.'P#Q' means 'P is neither greater than nor equal to Q'.'P$Q' means 'P is neither smaller than nor greater than Q'.'P*Q' means 'P is not greater than Q'.'P%Q' means 'P is not greater than Q'.Statements: M $ K, D * K, R # KConclusions: I. D $ M II. m % D
Answer: Option C. -> if either conclusion I or II is true.
M = K -- (i); D ≤ K -- (ii); R < K -- (iii)from (i) and (ii), we getM = K ≥ D => M ≥ DHence, either M > D (conclusion II) or M = D (conclusion I) is true.
Question 173. In the following questions, the symbols, @, #, $, * and % are used as illustrated below:'P@Q' means 'P is not smaller than Q'.'P#Q' means 'P is neither greater than nor equal to Q'.'P$Q' means 'P is neither smaller than nor greater than Q'.'P*Q' means 'P is not greater than Q'.'P%Q' means 'P is not greater than Q'.Statements: H $ K, T # H, W * TConclusions: I. K % W II. T # K
Answer: Option E. -> if both the conclusions I and II are true.
H = K -- (i); T < H -- (ii); W ≤ T -- (iii)From (i), (ii) and (iii), we getK = H > T ≥ W => K > W (conclusion I) and T < K (conclusion II).
Question 174. In the following questions, the symbols, @, #, $, * and % are used as illustrated below:'P@Q' means 'P is not smaller than Q'.'P#Q' means 'P is neither greater than nor equal to Q'.'P$Q' means 'P is neither smaller than nor greater than Q'.'P*Q' means 'P is not greater than Q'.'P%Q' means 'P is not greater than Q'.Statements: N % A, A # L, F $ NConclusions: I. L % A II. F % A
Answer: Option B. -> if only conclusion II is true.
N > A -- (i); A < L -- (ii); F = N -- (iii)From (i) and (iii),we get:F = N > A => F > A (conclusion II). But no specific relation can be obtained between L and F. Hence, conclusion I is not necessarily true.
Question 175. 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: B + D, D @ N, N $ HConclusions: I. H © D II. H © N
Answer: Option B. -> if only conclusion II is true.
B < D -- (i); D > N -- (ii); N ≤ H -- (iii)From equations (ii) and (iii), we can't obtained any specific relation between H and D. Hence, conclusion I (H ≥ D) is not true. But conclusion II (H ≥ N) follows from equation (iii).
Question 176. 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: K © M, M ∆ R, R ? TConclusions: I. K © T II. M ? T
Answer: Option D. -> if neither conclusion I nor II is true.
Combining all the equations, we getK ≥ M ≠R = T => M ≠TFrom this we can't get any specific relation between K and T. Hence, conclusion I is not true. Conclusion II is false since M ≠T.
Question 177. In the following questions, the symbols, @, #, $, * and % are used as illustrated below:'P@Q' means 'P is not smaller than Q'.'P#Q' means 'P is neither greater than nor equal to Q'.'P$Q' means 'P is neither smaller than nor greater than Q'.'P*Q' means 'P is not greater than Q'.'P%Q' means 'P is not greater than Q'.Statements: B * D, D $M, F % MConclusions: I. B #M II. F > B
Answer: Option B. -> if only conclusion II is true.
B ≤ D -- (i); D = M -- (ii); F > M -- (iii)From (i), (ii) and (iii), we get:F ≥ M = D ≥ B => B ≤ M and F > B (conclusion II).
Question 178. 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: M © K, K @ P, P $ NConclusions: I. M @ N II. M ? N
Answer: Option D. -> if neither conclusion I nor II is true.
M ≥ K -- (i); K > P -- (ii); P ≤ N -- (iii)combining (i) and (ii), we getM ≥ K > P -- (iv)From (iii) and (iv), no specific relation can be obtained between M and N. Hence, conclusion I (M > N) and conclusion II (M = N) are not true.
Question 179. 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: T $ M, M ? Q, Q + RConclusions: I. Q @ T II. Q ? T
Answer: Option E. -> if both the conclusions I and II are true.
T ≤ M -- (i); M = Q -- (ii); Q ≤ R -- (iii)Combining (i) and (ii), we getM = Q ≥ T => Q > T (conclusion I)or Q + T (conclusion II)
Answer: Option C. -> 19 ÷ 5 + 4 – 2 x 4 = 13
Answer: (c)
- ⇒ ÷, + ⇒ x, ÷ ⇒ x, - ⇒ +,
From option (a), 19 + 5 - 4 x 2 ÷ 4 = 11
⇒ 19 x 5 ÷ 4 + 2 - 4 = 11
⇒ 95/4 + 2 - 4 ≠ 11
From option (b),
19 x 5 - 4 ÷ 2 + 4 = 16
⇒ 19 + 5 ÷ 4 - 2 x 4 = 16
⇒ 19 + 5/4 - 8 ≠ 16
From option (c),
19 ÷ 5 + 4 - 2 x 4 = 13
⇒ 19 - 5 x 4 ÷ 2 + 4 = 13
⇒ 19 - 5 x 2 + 4 = 13
⇒ 19 - 10 + 4 = 13
Therefore 13 = 13
As,we got our answer, there is no need to check option (d).
Answer: (c)
- ⇒ ÷, + ⇒ x, ÷ ⇒ x, - ⇒ +,
From option (a), 19 + 5 - 4 x 2 ÷ 4 = 11
⇒ 19 x 5 ÷ 4 + 2 - 4 = 11
⇒ 95/4 + 2 - 4 ≠ 11
From option (b),
19 x 5 - 4 ÷ 2 + 4 = 16
⇒ 19 + 5 ÷ 4 - 2 x 4 = 16
⇒ 19 + 5/4 - 8 ≠ 16
From option (c),
19 ÷ 5 + 4 - 2 x 4 = 13
⇒ 19 - 5 x 4 ÷ 2 + 4 = 13
⇒ 19 - 5 x 2 + 4 = 13
⇒ 19 - 10 + 4 = 13
Therefore 13 = 13
As,we got our answer, there is no need to check option (d).
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