Directions
(1 – 4): Read the information given and answer the
following questions.
The Greek letters α, β, λ, μ, Ω, φ and π not
necessarily in that order, stand for seven consecutive integers from 1 to 10, μ
is 3 less than α, β is the middle term. φ is as much less than β as λ is
greater than μ, π is greater than φ.
1. The fifth integer is
A) α
B) λ
C) μ
D) Ω
E) φ
2. α is as much greater than φ as which integer is
less than π?
A) α
B) β
C) λ
D) μ
E) Ω
3. If α = 7, the sum of φ and π is
A) 8
B) 11
C) 12
D) 14
E) 16
4. The greatest possible value of λ is how much greater than the smallest
possible value of μ ?
A) 2
B) 3
C) 4
D) 5
E) 6
Directions
(5 – 9): In the following
question assuming the given statements to be true, find which of the conclusion
among given three conclusions is /are definitely true and then give your
answers accordingly.
5. Statements: K ≥ J; L = M; O < N; K <L; K
< P; M ≥ N
Conclusions: I. M < O II. J < L III. J
> L IV. N < P
A) None is true
B) Only II and IV are true
C) Only I and IV is true
D) Only II is true
E) Only III is true
6. Statements: 1 > X; Y = 8; 6 ≤ 1; 8 < Z
Conclusions:
I. 8 ≥ Y II. 6 >
X III. X > Y
A) None is true
B) Only I and II are true
C) Only II and III are true
D) Only III and I are true
E) All are true
7. Statements: J > K ≥ M< O; K ≤ L; M ≥ N; A > N; B
< C; B < N
Conclusions: I. L ≥ N II. B < O III. J > B
A) None is true
B) Only I is true
C) Only II is true
D) Only I and III is true
E) All are true
8. Statements: T ≤ U; V < W > X; U = V; Y ≥ Z
> T
Conclusions: I. Z < U II. U < Y
A) Only conclusion I is true.
B) Only conclusion II is true.
C) Either conclusion I or II is true.
D) Neither conclusion I nor II is
true.
E) Both the conclusion I and II are
true.
9. Statement: M ≥ Q > T ≥ S < O ≤ W < X; P ≥ N < Y ≥ Z ≥
V ≥ U ≥ R
Conclusions:
I. M >
S II. R ≤ X III. Y <
V IV. T ≥ O V. T > Y
A) Only conclusion (I) is true.
B) Neither conclusion (I) nor
conclusion (III) is true.
C) Only conclusion (III) is true.
D) Only conclusion (II) is true.
E) All conclusion (I), (II), (III),
(III) and (V) are true.
Solutions:
(1 – 4):
Alphabets: α, β, λ, μ, Ω,
φ and π
Numbers: 1 to 10
Condition:
1. They stand for 7
consecutive integers.
2. μ is 3 less than α ⇒ α – μ = 3 ⇒ α > μ
3. β is the middle term.
4. φ is as much less than
β as λ is greater than μ ⇒ β – φ = λ – μ ⇒ β ≫ φ and λ > μ
5. π is greater than φ ⇒ π > φ
Since we don’t know the
first number for given consecutive number. So, we’ll arrange alphabets using
given order but wouldn’t assign numbers.
1) β is the middle term.
2) α – μ = 3
Possibility 1
Alphabet


μ


β

α



Position

1st

2nd

3rd

Middle

5th

6th

7th

Possibility 2
Alphabet



μ

β


α


Position

1st

2nd

3rd

Middle

5th

6th

7th

3) β – φ = λ – μ
Possibility 1
Alphabet


μ

φ

β

α



Position

1st

2nd

3rd

Middle

5th

6th

7th

But no place for λ. Hence
this possibility is eliminated.
Possibility 2
Alphabet


φ

μ

β

λ

Α


Position

1st

2nd

3rd

Middle

5th

6th

7th

4) π > φ
Alphabet

Ω

φ

μ

β

λ

Α

π

Position

1st

2nd

3rd

Middle

5th

6^{th}

7th

1. B) Clearly,
5th integer is λ.
2. D) α
– φ= π – x⇒ 6 – 2 = 7 – x⇒ x = 3rd = π.
3. B) If
α = 7 (6 + 1) then φ = 2 + 1 = 3; π = 7 + 1 = 8 ⇒ φ + π = 8 + 3 = 11
4. E) Greatest
possible value of λ is smallest possible value of μ Greatest value of λ
can be 8 and smallest value of μ can be 3 ⇒ 8 – 3 = 5.
5. D) Given
statements: K ≥ J; L = M; O < N; K < L; K < P ; M ≥ N
On combining: J ≤ K <
L = M ≥ N > O; K < P
Conclusions:
I. M < O → False (as M
≥ N > O)
II. J < L → True (as J
≤ K < L)
III. J > L → False (as
J ≤ K < L)
IV. N < P → False (No
relation between N and P)
Therefore, conclusion II
is true.
6. A) Given
statements: 1 > X; Y = 8; 6 ≤ 1; 8 < Z
On combining: Z > 8 =
Y; 6 ≤ 1 > X,
Conclusions:
I. 8 ≥ Y → False (as 8 =
Y → thus 8 cannot be greater than Y)
II. 6 > X → False (as
6 ≤ 1 > X → thus no direct relationship between 6 and X can be obtained)
III. X > Y → False (no
direct relationship between Y and X can be obtained)
Therefore, none of the
conclusions is true.
7. E) Given
statements: J
> K ≥ M< O; K ≤ L; M ≥ N; A > N; B < C; B < N
On combining: J > K ≤
L; K ≥ M < O; A > N ≤ M; N > B < C
Conclusions:
I. L ≥ N → True (as K ≤ L
and K ≥ M and N ≤ M → N ≤ M ≤ K ≤ L → N ≤ L)
II. B < O → True (as M
< O and N ≤ M and N > B → O > M ≥ N > B → O > B)
III. J > B → True (as
J > K and K ≥ M and N ≤ M and N > B → J > K ≥ M ≥ N > B → J > B)
Therefore, all the
conclusions follow.
8. D) Given
Statements:
T ≤ U; V < W > X; U
= V; Y ≥ Z = T
⇒ Y ≥ Z > T ≤ U = V < W > X
Conclusions:
I. Z < U → Z > T ≤
U → hence relationship between Z and U cannot be determined.
II. U < Y → Y ≥ Z >
T ≤ U → Y > T ≤ U → hence relationship between U and Y cannot be determined.
Hence none of the
conclusion follow.
9. A) Given
statements: M ≥
Q > T ≥ S < O ≤ W < X; P ≥ N < Y ≥ Z ≥ V ≥ U ≥ R
On combining: M ≥ Q
> T ≥ S < O ≤ W < X, P ≥ N < Y ≥ Z ≥ V ≥ U ≥ R
Conclusion:
I. M > S → True as it
is given that M ≥ Q > T ≥ S.
II. R ≤ X → Not true as
there is no definite relation between R and X.
III. Y < V → Not true
as it is given that Y ≥ Z ≥ V.
IV. T ≥ O → Not true as
it is given that T ≥ S < O therefore there is no definite relation between
them
V. T > Y → Not true as
there is no definite relation between T and Y.