Question
If the 5-digit number 693XY is divisible by 3, 7, and 11,
then what is the value of X + 2Y?Solution
ATQ;
The 5-digit number 693XY is divisible by 3, 7, and 11.
Divisibility rule of 3: The sum of digits must be a multiple of 3.
6+9+3+X+Y=18+X+Y
So, X + Y must be one of {0, 3, 6, 9, 12, 15, 18}.
Divisibility rule of 11: The difference between the sum of alternate digits must be divisible by 11.
(6+3+Y)−(9+X)=0
9+Y−9−X=0
Y−X=0
X=Y
From X + Y = 6, and X = Y, we get:
2X=6⇒X=3,Y=3
Checking divisibility by 7:
The number 69333 is divisible by 7.
Finding X + 2Y:3+2(3)=3+6=9
Statements: U $ N © C @ H © Y
Conclusions:
I. U © H
II. C # U
III.H © U
Statements: C ≥ E > M ≤ Z < B; G ≥ Z > K
Conclusions: I. C > K II. G ≥ B ...
Statements: E = L ≤ G < I = H; E ≥ N < A; W ≥ P ≥ M > I
Conclusions:
I. E < W
II. A ≥ M
III. N < P
Statements: J > K > L, L < M > X, X = Y > Z
Conclusion:
I. L = Z
II. J > Y
Statements:
A < B < Z < K ≤ B < H; K > N ≥ P
Conclusions:
I) A < P
II) Z ≥ N
Statements: P ≥ Q ≥ R = S, Q ≥ T > U ≥ V
Conclusion:
I. P ≥ V
II. P > V
Statements: J @ K, K $ L, L & M, M % N
Conclusions: I. K @ M II. N & J
...If “M % N # O © P @ S © T $ W” is true then which of the following is definitely not true?
(i) M # P
(ii) O © T
(iii) N #...
Statements: J < K = L ≥ M ≥ P; F ≥ K < G
Conclusion I. J < G II.F ≥ P
...Which of the following symbols should replace the sign (@) respectively in the given expression in order to make the expression Y ≥ Z and D > K defin...
