Logical Reasoning Modal Questions
Statements and Conclusions
Directions (Q.1 – 5): In each of the questions below are
given four statements followed by three conclusions numbered I, II & III.
You have to take the given statements to be true even if they seem to be at variance
from commonly known facts. Read all the conclusions and then decide which of
the given conclusions logically follows from the given statements disregarding commonly
known facts.
1. Statements:
All chillies are garlics.
Some garlics are onions.
All onions are potatoes.
No potato is ginger.
Conclusions:
I. No onion is ginger.
II. Some garlics are potatoes.
III. Some chillies are potatoes.
1) Only I follows
2) Only II follows
3) Only I & II follow
4) Only I & III follow
5) All follow
2. Statements:
Some keys are locks.
Some locks are numbers.
All numbers are letters.
All letters are words.
Conclusions:
I. Some locks are letters.
II. Some words are numbers.
III. All numbers are words.
1) Only I & II follow
2) Only II & III follow
3) Only I & III follows
4) Only I & either II or III follows
5) All follow
3. Statements:
Some windows are doors.
All doors are walls.
No wall is roof.
All roofs are shelters.
Conclusions:
I. Some windows are walls.
II. No wall is shelter.
III. No door is shelter.
1) None follows
2) Only II & III follow
3) Only I & III follow
4) Only I follows
5) None of these
4. Statements:
All bottles are jars.
Some jars are pots.
All pots are taps.
No tap is tank.
Conclusions:
I. No pot is tank.
II. Some jars are tanks.
III. Some bottles are pots.
1) Only I & III follow
2) Only I & II follow
3) Only II & III follow
4) All follow 5) None of these
5. Statements:
Some fish are crocodiles.
Some crocodiles are snakes.
No snake is tortoise.
All tortoises are frogs.
Conclusions:
I. No snake is frog.
II. Some snakes are fish.
III. Some fish are frogs.
1) None follows
2) Only I & II follow
3) Only II & III follow
4) Only I & III follow
5) None of these
Directions (Q.6 –
10): These questions are based on the following information:
‘A @ B’ means ‘A is added to B’.
‘A ★ B’ means ‘A
is multiplied by B’.
‘A # B’ means ‘A is divided by B’.
‘A $ B’ means ‘B is subtracted from
A’.
In each question, some information is given. You have to
find out which expression correctly represents the statement.
6. Total age of 12
boys is ‘X’ and the total age of 13 girls is ‘Y’. What is the average age (A)
of all the boys and girls together?
1) A = (X@Y)#25 2) A = (X$Y)#25
3) A = (X@Y)★25
4) Cannot be determined 5) None
7. Population of state M (P1) is less than half of
population of state N (P2) by 1,50,000
1) P2 = (P1#2)$1,50,000
2) P1= (P2#2)@1,50,000
3) P1= (P2#2)$ 1,50,000
4) P2 = (P1#2)@ 1,50,000
5) None of these
8. Number of boys (B)
in a class is equal to one – fourth of three times the number of girls (G) in
the class.
1) B = (3#G)★4 2) B = (3★G)@4
3) B = (3★G)#4 4) B = (3$G)#4
5) None of these
9. Salary of Mr. X
(S1) is more than 40% of Mr. Y’s salary (S2) by Rs.8,000
1) S1 = [S2★(400@100)]#8,000
2) S1 = [S2★(400#100)]@8,000
3) S2 = [S1★(400#100)]@8,000
4) S2 = [S1★(400@100)]#8,000
5) None of these
10. Marks obtained by
Sujit in History (H) are 85% of his marks obtained in Science (M).
1) H = (100#85)★M
2) H = 85★100★M
3) H = 85#100#M
4) H = (85#100)★M
5) None of these Directions (Q.11 – 15): In the following
questions, the symbols @, #, $,© and % are used with different meanings as
follows:
‘P @ Q’ means ‘P is not smaller than Q’.
‘P # Q’ means ‘P is not greater than Q’.
‘P $ Q’ means ‘P is neither greater than nor equal to Q’.
‘P © Q’ means ‘P is neither smaller than nor equal to 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 two conclusions I and II given below
them is/are definitely true?
Give answer (1):
if only conclusion I is true.
Give answer (2):
if only conclusion II is true.
Give answer (3):
if either conclusion I or II is true.
Give answer (4):
if neither conclusion I nor II is true.
Give answer (5):
if both conclusions I and II are true.
11. Statements: V
$ W, W @ T, T # H
Conclusions: I. V
© T II. H % W (Ans : 4)
12. Statements: H
© M, M @ E, E $ C
Conclusions: I. C
@ M II. H © E (Ans:2)
13. Statements: N
@ J, J % R, R © H
Conclusions: I. R
# N II. N © H (Ans:5)
14. Statements: L
@ K, K © A, A $ W
Conclusions: I. W
$ L II. L # W (Ans:4)
15. Statements: J
# R, R © D, D@ F
Conclusions: I. F $ R II. F % R (Ans:1)
Explanation:
1.3; First and third Premises are Universal Affirmative (A –
type).
Second Premise is Particular Affirmative ( I – type).
Fourth Premise is Universal Negative ( E – type).
Some garlics are onions. All
onions are potatoes
I + A⇒ I –
type Conclusion.
“Some garlics are potatoes.”
This is Conclusion II.
All onions are potatoes.
No potato is ginger.
A + E ⇒E –
type Conclusion
“No onion is ginger”.
2.5; First and second Premises are Particular Affirmative (I
– type).
Third and fourth Premises are Universal Affirmative (A –
type).
Some locks are numbers.
All numbers are letters.
I + A = I – type Conclusion.
“Some locks are letters”.
This is Conclusion I.
Some locks are letters.
All letters are words.
I + A⇒ I –
type Conclusion.
“Some locks are words.”
“All numbers are letters.”
All letters are words.
A + A⇒A –
type Conclusion.
“All numbers are words.”
This is Conclusion III.
Conclusion II is Converse of this Conclusion.
3.4; First Premise is Particular Affirmative (I – type).
Second and fourth Premises are Universal Affirmative (A –
type).
Third Premise is Universal Negative (E – type).
Some windows are doors.
All doors are walls.
I + A = I – type Conclusion.
“Some windows are walls.” This is Conclusion I.
All doors are walls.
No wall is root.
A + E = E – type Conclusion. “No door is roof.”
No wall is roof.
All roofs are shelters.
E + A = O∗ - type Conclusion.
“Some shelters are not doors.”
No wall is roof.
All roofs are shelters.
“Some shelters are not walls.”
4.5; First and third Premises are Universal Affirmative (A –
type).
Second Premise is Particular Affirmative (I – type).
Fourth Premise is Universal Negative (E – type).
Some jars are pots.
All pots are taps.
I + A⇒ I –
type Conclusion.
“Some jars are taps.”
All pots are taps. No tap is tank.
A + E = E – type Conclusion. “No pot is tank.”
This is Conclusion I.
5.1; First and second Premises are Particular Affirmative (I
– type).
Third Premise is Universal Negative (E – type).
Fourth Premise is Universal Affirmative (A – type).
Some crocodiles are snakes.
No snake is tortoise.
All tortoises are frogs.
I + A = E - type Conclusion.
“Some crocodiles are not tortoises.”
No snake is tortoise.
All tortoises are frogs.
E + A = O* - type Conclusion.
“Some frogs are not snakes.”
6.1; Average age of all the boys (X +Y)
and girls (A) = (A) = ⎯⎯25 ⇒A = (X@Y)#25
7.3; P1 = P2⎯P2−
1,50,000
⇒ P1= (P2#2)$ 1,50,0008.3;
B = 1⎯4× 3G = 3G⎯4⇒
B = (3 ★
G) # 49.2;
S1 = 40⎯100 × S2+ 8,000
⇒ S1 = [ S2 ★ (400 # 100)]@8,00010.4;
H = 85⎯100× M
⇒ H = (85#100) ★ M( 11 – 15 ):
P @ Q ⇒ P ≥ Q
P # Q ⇒ P ≤ Q
P $ Q ⇒ P < Q
P © Q ⇒ P > Q
P % Q ⇒ P = Q
11.4; V $ W ⇒ V < W
W @ T ⇒ V ≥ T
T # H ⇒ T≤ H
Therefore, V < W ≥ T ≤ H
Conclusions:
I. V © T ⇒ V > T : Not true
II. H % W ⇒ H = W : Not true.
12.2; H © M ⇒ H > M
M @ E ⇒ H ≥ M
E $ C ⇒ E < C
Therefore, H > M ≥ E < C
Conclusions:
I. C © M ⇒ C > M : Not true
II. H © E ⇒ H > E : True
13.5; N @ J ⇒ N ≥ J
J % R ⇒ J = R
R © H ⇒ R > H
Therefore, N ≥ J = R > H
Conclusions:
I. R # N ⇒ R ≤ N
: True
II. N © H ⇒ N > H : True
14.4; L @ K ⇒ L ≥ K
K © A⇒ K > A
A $ W ⇒A < W
Therefore, L ≥ K > A < W
Conclusions:
I. W $ L⇒ W < L : Not true
II. L # W ⇒ L ≤ W
: Not true
15.1; J # R ⇒ J ≤ R
: Not true
R © D ⇒ R > D
D @ F ⇒ D ≥ F
Therefore, J ≤ R > D ≥ F
Conclusions:
I. F $ R ⇒ F < R : True
II. F % R ⇒ F = R : Not true.
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