IN A STACK OF BOARDS AT A LUMBER YARD

[Guest]

IN A STACK OF BOARDS AT A LUMBER YARD, THE 20TH BOARD COUNTING FROM THE TOP OF THE STACK IS IMMEDIATELY BELOW THE 16TH BOARD COUNTING FROM THE BOTTOM OF THE STACK. HOW MANY BOARDS ARE IN THE STACK?

THE ANSWER IS 34- GMAT PREP TEST #1

CAN YOU PLEASE EXPLAIN HOW I CAN GO ABOUT SOLVING THIS PROBLEM... THANKS

[mdesiato]

To solve this problem you need to understand that boards are double counted 2 times. The 20th board was counted in the set "16 from the bottom", and the 16th board was counted in the set "20 from the top". So, (20-1) + (16-1) = 34.

[Guest]

COULD YOU PLEASE ELABORATE ON THE REASON AS TO WHY YOU ARE SUBTRACTING 1 FROM EACH ONE AND THEN ADDING THEM UP. IS IT BECAUSE THEY ARE CONSECUTIVE? OR FOLLOW SOME PATTERN? GREATLY APPRECIATED...

[RonPurewal]

COULD YOU PLEASE ELABORATE ON THE REASON AS TO WHY YOU ARE SUBTRACTING 1 FROM EACH ONE AND THEN ADDING THEM UP. IS IT BECAUSE THEY ARE CONSECUTIVE? OR FOLLOW SOME PATTERN? GREATLY APPRECIATED...

make a diagram in which you label the boards as follows. the blue numbers count from the top, and the orange numbers count from the bottom.

1
2
3
4
.
.
.
17
18
19 16
20 15
14
13
.
.
.
3
2
1

this diagram should make it clear that the two middle boards - the one that is blue19/orange16 and the one that is blue20/orange15 - are counted twice. therefore, 20 + 16 = 36 is two greater than the actual number of boards.
thus, 34 boards.
(there's a dennis rodman joke waiting to be made here)