elitmus
Exam
Logical Reasoning
Cryptography
a multiplication is given below where each letter represents a single digit and no two no.s are represented by the same letter:
W H Y
N U T
-------------------
O O N P
O Y P Y
O U H A
-------------------
O N E P O P
i)Which of these is not divisible by 2?
a)W b)Y c)U d)N
ii)One of those digits appear only once in the multiplication except:
a)2 b)5 c)6 d)8
iii)Which of these can be sides of a triangle?
a)NYT b)OWY c)EUO d)APW
Read Solution (Total 15)
-
- logical simple solution:-
after analyzing the multiplication the basic logical deductions are:-
1. O + A = 9. (AS O+P+A=P which is only possible if O+A=9)
2. U=6. as U * Y= Y. SO EITHER U=1 OR U=6(U=1 not possible as U*(W H Y)=O Y P Y)
SINCE U=6, THEN Y MUST BE AN EVEN INTEGER.(6 * 2 =10 + 2, 6 * 4= 20 +4 ...)
3. Also from column 2, N + Y = 10 + O.
4. Also A and P must be even as Y is even.
ALGORITHM:-
# if there is a carry from column 4 to column 5 then:-
1 + O + U = N. implies O + 7 = N (AS U=6)...equation...4.
since there is no carry from column 5 to column 6 last column.
implies... O can be 0, 1 or 2 only.
IF O=0, THEN N=7, THEN Y=3 (NOT POSSIBLE AS Y IS EVEN).
IF O=1, THEN N=8, THEN Y=3(NOT POSSIBLE AGAIN)
IF O=2, THEN N=9, THEN Y=3(NOT POSSIBLE AGAIN)
since equation 4 does not satisfies the basic deductions(1,2,3) so it must be wrong.
# so there is no carry from column 4 to column 5...which implies:-
O + U = N.. which means O + 6 = N. ....equation...5.
IF O =0, THEN N=6 (NOT POSSIBLE AS U=6)
IF O =1, THEN N=7, THEN Y=4, A= 8 (even) ... (POSSIBLE AS Y and A IS EVEN).
IF O=2, THEN N=8, THEN Y=4, BUT A=7 SO NOT POSSIBLE.
IF O=3, THEN N=9, THEN Y=4, A=6(even) but since U=6 already(NOT POSSIBLE)
# SO O=1, U=6, N=7, A=8...
NOW H must be a number less than 5..(0,1,2,3,4)
H=1 OR H=4 (NOT POSSIBLE...AS O=1 AND Y=4 )
IF H=0, then E=6 as U= 6, (NOT POSSIBLE)
IF H=2, then E=8 as A=8, (NOT POSSIBLE)
so H=3.
now 7 * (W 3 4)= 1638...implies 7 *w + 2 = 16....implies w=2.
T can be 0 or 5 only...but T cannot be zero so T=5...implies p=0.
so the final multiplication is...
2 3 4
* 7 6 5...
- 10 years agoHelpfull: Yes(13) No(2)
- 234
*765
------
1170
1404
1638
-----
179010
i)->d
ii)->c
iii)->...? - 10 years agoHelpfull: Yes(7) No(5)
- W=2 H=3 Y=4 N=7 U=6 T=5 P=0 O=1 A=8
- 10 years agoHelpfull: Yes(1) No(5)
- how to assign a value 234 to WHY ?
any 1 explain me please......
- 10 years agoHelpfull: Yes(1) No(2)
- arjun plz tell me ,how to get in 2nd queation=6 plz elaborate 2nd answer
- 10 years agoHelpfull: Yes(1) No(1)
- 723
*432
_____
1446
2169
2892
_________
312336 - 10 years agoHelpfull: Yes(1) No(3)
- w=2, h=3, y=4,n=7, u=6, t=5
- 10 years agoHelpfull: Yes(0) No(3)
- 234
*765
----------------
1170
1404
1638
----------
179010 - 10 years agoHelpfull: Yes(0) No(2)
- NYT is the side of a triangle because 4+5>7. therefore (7,4,5) is the side of triangle.
- 10 years agoHelpfull: Yes(0) No(1)
- (why*nut)=234*765
anser(1) - option-(d)so N=7 not divisible by 2
anser(2)- option- (d)8 is appear ones
answer(3)- option - (a)-nyt(7,4,5) - 10 years agoHelpfull: Yes(0) No(2)
- It is cleat that (D+1)=A.
So there are 8 possible values of (D,A)
(1,2)(2,3)(3,4)(4,5)(5,6)(6,7)(7,8)(8,9).
(1,2) is not possible..
So when u substitute D=2 and A=3... u will get the answer in 2 minutes :) - 10 years agoHelpfull: Yes(0) No(5)
- How NYT is the side of a triangle. Can anybody explain.
- 10 years agoHelpfull: Yes(0) No(0)
- 1) d
2) c
3) a - 10 years agoHelpfull: Yes(0) No(0)
- 234
765
..............
1170
1404
1638
............
179010 - 10 years agoHelpfull: Yes(0) No(0)
- NYT will be the side of triangle from the properties of the triangle.. ie, sum of any two sides will be always greater then its third side.. so here N=7, Y=4, T=5... 7+4>5, 4+5>7, 7+5>4
- 9 years agoHelpfull: Yes(0) No(0)
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