Number System - Questions & Discussions

A Salesman enters the quantity sold and the price into the computer. Both the numbers are two-digit numbers. Once, by mistake, both the numbers were entered with their digits interchanged. The total sales value remained the same, i.e. Rs. 1148, but the inventory got reduced by 54.

1. What is the actual price per piece?
a. 82 b. 41 c. 56 d. 28
2. What is the actual quantity sold?
a. 28 b. 14 c. 82 d. 41

Find the value of 1/ (1+1/ (3-4/ (2+1/ (3-1/2)))) + 3/ (3-4/ (3+ (1/ (2-1/2))))
a. 13/7 b. 15/7 c. 11/21 d. 17/28



ans:13/7

2/7+11/7=13/7
ans:13/7

2/7+11/7=13/7


cud u elaborate a little...thanks.
A Salesman enters the quantity sold and the price into the computer. Both the numbers are two-digit numbers. Once, by mistake, both the numbers were entered with their digits interchanged. The total sales value remained the same, i.e. Rs. 1148, but the inventory got reduced by 54.

1. What is the actual price per piece?
a. 82 b. 41 c. 56 d. 28
2. What is the actual quantity sold?
a. 28 b. 14 c. 82 d. 41


The actual price per piece is 14
The actual quantity sold is 82
1148=2^2*7*41
now by hit nd trial u will easily get d answer...........
A Salesman enters the quantity sold and the price into the computer. Both the numbers are two-digit numbers. Once, by mistake, both the numbers were entered with their digits interchanged. The total sales value remained the same, i.e. Rs. 1148, but the inventory got reduced by 54.

1. What is the actual price per piece?
a. 82 b. 41 c. 56 d. 28
2. What is the actual quantity sold?
a. 28 b. 14 c. 82 d. 41

answers:
1)41
2)28

1)41
2)28

The inventory was reduced by 54 so the difference between the interchanged no and original no is 54.So 41 and 14 are eliminated.
The remaining nos are 82 and 28.Since the inventory was reduced by 54 the original no is smaller no among the 2 so its 28i.e 82-28=54
Since the no of items is 28 the price per item is 1148/28=41
janvats Says
cud u elaborate a little...thanks.

1/ (1+1/ (3-4/ (2+1/ (3-1/2))))

on solving dis

1/(1+1/(3-4/(2+1/(6-1)/2=1/(1+1(3-4/(2+1(5/2)=1/(1+1(3-4/(2+2/5)=1/(1+1/3-4(2+2/5)

=1/1+1/(3-4/(12/2)=1/(1+1/(3-4*5/12)=1/(1+1/(3-20/12))=1/(1+1/(36-20/12))=1+1/16/12

=2/7

same way other part 3/3-4/(9+2)/3
=3/3-(4*3)/11

=3*11/33-12

=11/7

uffffffffffffffffffffffffffffffffffffffffff.....thakk gaye 😞
answers:
1)41
2)28

1)41
2)28

The inventory was reduced by 54 so the difference between the interchanged no and original no is 54.So 41 and 14 are eliminated.
The remaining nos are 82 and 28.Since the inventory was reduced by 54 the original no is smaller no among the 2 so its 28i.e 82-28=54
Since the no of items is 28 the price per item is 1148/28=41


Am not gettin how u deduced that d original number is smaller........
PearlCrystal Says
Please share your approach naga.



jus sample to smaller number

9^2 = 81 ---> 1*9 = 9

99^2 = 9801--->2*9 = 18

similarly (99... 2009 digits)^2 ---> 9*2009 = 18081
A Salesman enters the quantity sold and the price into the computer. Both the numbers are two-digit numbers. Once, by mistake, both the numbers were entered with their digits interchanged. The total sales value remained the same, i.e. Rs. 1148, but the inventory got reduced by 54.

1. What is the actual price per piece?
a. 82 b. 41 c. 56 d. 28
2. What is the actual quantity sold?
a. 28 b. 14 c. 82 d. 41

Question says that the the inventory got reduced by 54 after the digits were interchanged which means it was showing more quantity as sold.
if the quantity originally sold = 10a+b then, b-a = 6.
Also, if the price is y then, (10a+b)*y = 1148.
From hit and trial we get 10a+b = 28 => y = 41.
So, actual price per piece = 41.
And the actual quantity sold = 28.

1.If xy+x+y=2,which of the following is true?
a)(x+1/y+1)>0
b)(x+2/y+2)>0
c)(x-1/y-1)>0
d)(x-2/y-2)>0

puys pls give the proper xplanation for eliminating oder options..

catwoman_09 Says
Am not gettin how u deduced that d original number is smaller........

let me ans

the options after elimination are 28 and 82
so as the inventory got reduced it cant be 28 (as 28 cant b reduced to 82 28hence it was 82 and the other ans is 28
470=10*47

8*10^88+8*10^87+8^86+-------------------------------------8

8(10^89-1)/9 mod 47

8(10^89-1)/9 =k

8*10^89=9k+8

(8*10^92)mod 47=1000(9k+ mod 47

9000k mod 47 =2

k=43

47 x+43=10y+8


y=47x+35/10

x=5,y=27

so remainder is 278

Can you explain the red part more clearly ???
Hi puys,
can any1 solve the problem in a lucid way?
N=888888888...89 digits % 470=?



N=888888888...89 digits

470 = 2 * 5 * 47

N/2 , the remainder is 0

N/5 , the remainder is 3

N/47 , the remainder is 4

2a = 5b + 3 = 47c + 4

10k + 8 = 47c + 4

hence the final remainder is (47 * 2) + 4 = 98

When 7^84 is divided by 342, what is the remainder?
a. 0 b. 1 c. 49 d. 341

470=10*47

8*10^88+8*10^87+8^86+-------------------------------------8

8(10^89-1)/9 mod 47

8(10^89-1)/9 =k

8*10^89=9k+8

(8*10^92)mod 47=1000(9k+ mod 47

9000k mod 47 =2

k=43

47 x+43=10y+8


y=47x+35/10

x=5,y=27

so remainder is 278


check the bold part .. it should be 47x - 43 or 47x + 4
N=888888888...89 digits

470 = 2 * 5 * 47

N/2 , the remainder is 0

N/5 , the remainder is 3

N/47 , the remainder is 4

2a = 5b + 3 = 47c + 4

10k + 8 = 47c + 4

hence the final remainder is (47 * 2) + 4 = 98


NAGA CAN U EXPLAIN ME THIS???
When 7^84 is divided by 342, what is the remainder?
a. 0 b. 1 c. 49 d. 341

option b. 1
x^24 mod x - 1 = 1, x = 7^3
remainder = 1
When 7^84 is divided by 342, what is the remainder?
a. 0 b. 1 c. 49 d. 341

the answer is 1
here is how
7^84=(7^3)^28
now 7^3=343
which gives a remainder of 1 upon divided by 342
so according to remainder theorem
the answer is 1^28=1
pgaucha Says
NAGA CAN U EXPLAIN ME THIS???

fermat theorem : for any prime number p , (p-1)times,same digit is repeated , then that number formed is exactly divisible by p ..

so 88(upto 46 digits) is perfectly divisible by 47..

so the same applies to 88(upto 92 digits)

in the question we have 88(upto 89 digits)

so x888 mod 47 = 0

since last digit is 8 , check for 4*47 = 188

last two digit is taken care

this means x8 leaves remainder 1 when divided by 47..

48 mod 47 = 1

so x = 4 ...

remainder is 4..

hope u got that ..revert me if u dont get it ..

cheers
When 7^84 is divided by 342, what is the remainder?
a. 0 b. 1 c. 49 d. 341


by remainder theorem answer is 1