It is possible to arrange eight of nine numbers 2,3,4,5,7,10,11,12,13 in the vacant squares of the 3 by 4 array shown below so that the arithmetic average of the numbers in each row and column is the same integer.
1
15
9
14
Which of the nine numbers must be left out when completing the array ?
In these questions the symbol @, *, % , #and $ are used with different meanings as follow : I). A@B means A is neither smaller than nor equal to B. II). A*B means A is not smaller than B. III). A%B means A is neither smaller than nor greater than B. IV). A#B means A is neither greater than nor equal to B. V). A$B means A is not greater than B.
In each question, four statements showing relationship have been given, which are followed by three conclusion I,II and III. Assuming that the given statements are true, find out which condition(s) is/are definitely true.
Q. No. 1:
Statements : F#L, L*D, D@E, E$H Conclusion : I. H$D II. F@H III. E#L
Answer: A H≥G, G>K, I<K, I =E Combining all the statements, we get H≥G>K>I=E => H >I (Combining I) And, E<G (Combining II) Hence conclusion I and II follow.
Q. No. 3:
Statements : M@J, J$F, F%E, E#L Conclusion : I. L@J II. J$L III. E%J
Answer: D R≤T, T>V, V=W, W≥Q => T>V=W≥Q => Q<T (Conclusion I) There is no specific relation between Q and R. So, Q is either less than R or greater than R or equal to R. And, conclusion II or III depics the above three relations. Hence I and either II or III are true.
Q. No. 5:
Statements : L#J, J@Q, Q*R, R$V Conclusion : I. L#Q II. Q*V III. J%V
Answer: D L<J, J>Q, Q≥R, R ≤V From all the statements there is no specific relations between L and Q, Q and V and J and V. Hence, none is true.
Symbols @,&, #, $ and % are used with following meanings. 1). P@Q means P is neither smaller than nor equal to Q. 2). P&Q means P is not greater than Q. 3). P#Q means P is neither greater than nor equal to Q. 4). P$Q means P is neither greater than nor smaller than Q. 5). P%Q means P is not smaller than Q. Now in each questions assuming the given statements to be true, find out which of the three conclusions I, II and III definitely follow and mark your answer accordingly.
Q. No. 1:
Statements : L@W, M#W, M%J Conclusion : I. M&L II. W%J III. L@J
Answer: C Here we have, G> H, H>=K, K<D => D>K Hence from first two equation we get, G>H>=K Again from G>H>=K and D>K we do not have any specific conclusion regarding D and H. But the conclusion II (D<H) and conclusion III (D>=H) make a complementary pair. Hence, either conclusion II or III follows.
Q. No. 4:
Statements :
F#D, D&K, R@K Conclusion :
I. F#K
II. R%D
III. R@F
Answer: D Here, we have B>=H, B = A, C>A From all we have, C>A=B>=H Hence only conclusion I follows.
In each of these questions the symbols @, #, $, % and * are used with different meanings as follow::
I). P@Q means P is not smaller than Q. II). P#Q means P is not greater than Q. III). P$Q means P is neither smaller than nor greater than Q. IV). P%Q means P is neither smaller than nor equal to Q. V). P*Q means P is neither greater than or equal to Q. In each question four statement showing relationships have been given, which are followed by four conclusions I, II, III and IV. Assuming that the given statement are true, find out which conclusion(s) is/are definitely true.
Q. No. 1:
Statement : L#T, T*D, D@H, H$K Conclusion : I. K*D II. K#D III. L*D IV. K$L
Answer: B Combining all the statements. We get the following two results D>T>=L and D>=H=K Here, there is definite relation between K and D i.e K=<D(conclusion II) and L and D (Conclusion III). Both conclusion I and IV are not true.
Q. No. 2:
Statement : E$F, F@I, I%K, L*K Conclusion :
I. E@I
II. L*F
III. F%K
IV. E%K
Answer: D According to the statements, we get the following results. E=F>=I,>K>L From the above relation we get, E>=I (conclusion I), L<F (conclusion II), F>K (conclusion III), E>K (conclusion IV). Hence all the conditions follows.
Q. No. 3:
Statement : R@J, J*F, F#M, M%V Conclusion :
I. J%V
II. R@M
III. J#V
IV. R*M
Answer: D Combining the statements we get the following three results, R>=J .......(i) M>=F>J .......(ii) M>V.......(iii) There is no definite relation between J and V. So, there are three possible relations between J and V i.e either J>V, J=V or J<V. Hence conclusion either I or III follows. Similarly, there is no definite relationship between R and M. So either R>M, R=M or R<M i.e either conclusion II or IV follows. Hence the either I or III and either II or IV follow.
Q. No. 4:
Statement : V%W, W#Z, Z@T, T$H Conclusion : I. Z%H II. V@Z III. V*Z IV. W$T
Answer: A From all the statements, we get the following three relations : V>W ...(i) Z>=W.....(ii) Z>=T=H.......(iii) There is no definite relation between Z and H, W and T and V and Z. So, conclusion I and IV does not follow. But in the case of V and Z. Either V>Z or V=Z or V<Z. Hence either conclusion II or III follows.
Q. No. 5:
Statement : H%L, L@Q, Q*R, R#N Conclusion : I. H@Q II. H%Q III. N@Q IV. N%Q
Answer: C Combining the given for statements we get, H>L>=Q .....(i) N>=R>Q......(ii) From (i) we get H>Q (conclusion II) and from (ii) we get N>Q (conclusion IV) hence, conclusion II and IV follow.
In each of the following questions two rows of numbers are given. resultant number in each row is to be worked out separately based on the following rules and the question below the row of numbers is to be answered. The operations of numbers progress from left to right. Resultant of the first operation is the input for the subsequent operation. Rules : i). If the composite odd number is followed by a prime number, the composite number is to be divided by the prime number. ii). If a composite number is followed by a number which is the perfect square, the two are to be added. iii). If an even number is followed by a prime number the two are to be multiplied. iv). If a composite odd number is followed by an even number the second number is to be subtracted from the first number. v). If a prime number is followed by any number, the two are to be multiplied. vi). If the even number is followed by a composite number the second number is to be subtracted from the first number.
Q. No. 1:
32 9 6 45 24 8 What is the difference between the resultants of the first and the second row ?
Answer: C P = 105 11 49 => 15 49 [use rule i] => 64 [use rule ii] Q = 64 18 7 => 46 7 [use rule vi] => 322 [use rule iii] Hence, the required resultant is 322
In these questions symbols #, @, $, *, % are to be used with different meanings as follow.
i). A#B means A is neither smaller than nor equal to B. ii). A@B means A is smaller than B. iii). A$B means A is not greater than B. iv). A*B means A is not smaller than B. v). A%B means A is neither smaller than nor greater than B. In each question three statement showing relationship have been given. Assuming that the given statements are true, find out which conclusion(s) is/are definitely true.
Q. No. 1:
Statements : T@J, J*M, M$B Conclusions : I. T#M II. J$B
Answer: D A>E........(i) A=F.........(ii) Q>=F.......(iii) On combining all we get, Q>=F=A>E. Hence both conclusion I(E<Q) and conclusion II (Q>=A) are true.
Q. No. 4:
Statements : L#M, M%D, D*Q Conclusions : I. M#Q II. Q@L
Answer: C F>=W ........(i) H>F.........(ii) H>R...........(iii) Combining i and ii, we get H>F>=W and H>R There is no definite relationship between W and R but in conclusion I ( W>R) and in conclusion II (W<=R). Hence, either of I and II is true.