Medium Puzzles 

Workings

Hint
The answer is 4 digits long, so what must G equal?

Answer
423 + 675 = 1098.

Reasoning
Remembering that:
   even + even = even
   odd  + odd  = even
   even + odd  = odd

To discuss individual letters, it's easiest to represent the sum as:
   A B C
   D E F +
————————
 G H I J

A + D has to be over 9, which means that G = 1.

B + E = I, is even + odd = odd, which means that we can't have a carry from C + F (otherwise it would have been even + odd + 1, which is even).

The 1 has already gone, so the smallest possible value for either C or F is 3, which means that the other can't be 7 or 9 (otherwise we'd have a carry).

Therefore, C and F are 3 and 5, but we don't know which is which. But we do now know that J = 8.

A + D = H, is even + even = even, which means that we can't have a carry from B + E. Therefore, E can't be 9, as this would force a carry. So E = 7.

I is the only remaining odd number, so I = 9.

Which means that B = 2.

Neither A nor D can be 0 (otherwise we would have two of the same digit). So, H = 0.

Therefore, A and D are 4 and 6 (but we don't yet know which is which).

Since the top row's digits have to add to 9, A can't be 6, so A = 4, making C = 3.

This makes the sum 423 + 675 = 1098.

Workings

Hint
In the word LOG, why might the L have be replaced with 50?

Answer
FO10.

Reasoning
If there is a Roman numeral, it is replaced by its modern equivalent.
   I = 1
   V = 5
   X = 10
   L = 50
   C = 100
   D = 500
   M = 1000

Double-Checking
CLICK = 100 50 1 100 K MILK  = 1000 1 50 K LOG   = 50 O G LIFE  = 50 1 F E ALIVE = A 50 1 5 E FOX   = F O 10

Workings

Hint
Try removing the spaces and punctuation.

Answers
ROME OR OSLO? ANDREW, JULIE, TO VISIT.
ROMEO ROSLO AND REW JULIET OVISIT
   = ROMEO AND JULIET

WARM TOO FEW, THE SUBWORLD SNEEZES
WAR MTO OF EW THE SUB WORLDS NEEZES
   = WAR OF THE WORLDS

AN I MALL? SHOPS, FAR MALLS?
ANIMAL LSHOPS FARM ALLS
   =ANIMAL FARM

GO NEXT, GO! WITHOUT OTHER I DWINDLE. GO!
GONE XTGO WITH OUTO THE RID WIND LEGO
   = GONE WITH THE WIND

WATER. SHIP, BOAT. STORM! DOWN RAIN!
WATERSHIP BOATSTORM DOWN RAIN
   = WATERSHIP DOWN

BRAVERY IN A NEW AGE, WORLD'S HOPE.
BRAVE RYINA NEW AGE WORLD SHOPE
   = BRAVE NEW WORLD

Workings

Hint
Try removing some letters.

Answer
Carrot.

Reasoning
Each of the other words remains a real word if you remove the first and last letter:
s-event-y b-raw-l c-love-r p-rope-r c-arro-t * s-win-g e-merge-d c-raft-y t-rave-l s-acre-d s-ton-e p-lung-e