Thread: easy Digits problem and Semicircle.. - fastest way to solve it? Otherwise easy

Hello

im not sure what the fastest way to solve this is..
please let me know.. thanks!



22. A and B are letters representing different digits from 1 to 9.
Given:

AB
X 7
-----
4BB


A-B=?


(I) 1
(2) 2
(3) 3
(4) -1

answer: 1
need 5 bc 7*5= 35.. b needs to be 5.
..
defiitely 5.
definitely need a 6 because 60 * 7 is 420 ish..
7 is too high
..
so 6-5 =1


not sure if this is the fastest way! thanks!


21.
A certain 2 digit number is known to be 3 times as great as the sum of its digits. What is the product of its digits?

1. 12
2. 14
3. 16.
4. 18

answer: 2

27 is 3x greater than 2+7 = 9.
2*7 is 14.

not sure how to do this FAST without going backwards?




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Semicircle.. shaded region

q21

the legs of a triangle ABC are 2 and 4. it is in a semicircle. and is painted white. the rest of the semicircle is black. what is the area of the black?

i know that answer must have -4 because 1/2 * 2 * 4 = 4.


the area..
2^2 + 4^2 = hyp^2
4 + 16 = 20, hyp is root 20
pi* (1/2 root 20 )^2 = total area.
20/4 = 5
so 5pi - 4??
huh
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PS is there a way to post pictures up here? other people did it and i'd like to know how!

I thinks its probably fastest the way you have done

22. A and B are letters representing different digits from 1 to 9.
Given:
AB
X 7
-----
4BB
B × 7 = B
B = 0 or 5
if B = 0 then A × 7 = 40
none of value of integer value satisfy the condition
so B = 5
A 5
× 7
---------
455
calculate directly 455/7 = 65
A = 6
or A × 7 + 3 (c/f) = 45
or A × 7 = 42
A = 6
A - B = 6 – 7 = – 1

(4) -1

A certain 2 digit number is known to be 3 times as great as the sum of its digits. What is the product of its digits?
Let the digits in the number be ab
then number is 10a + b
10a + b = 3(a + b)
10a + b = 3a + 3b
7a = 2b
a = 2, b = 7
a × b = 14

2. 14
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