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Collection of questions [#permalink] New post  15 Nov 2012, 07:30
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A number when divided by 84 leaves a remainder of 57. What is the remainder when the same number is divided by 12?

(A) 7
(B) 8
(C) 9
(D) 11
(E) Cannot be determined



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Re: Collection of questions [#permalink] New post  Updated on: 15 Nov 2012, 08:36
The diagonal of a square is approximately how much less than the two of its sides combined ?

(A) 30%
(B) 40%
(C) 29%
(D) 39%
(E) 66%
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Originally posted by vomhorizon on 15 Nov 2012, 08:22.
Last edited by vomhorizon on 15 Nov 2012, 08:36, edited 1 time in total.
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Re: Collection of questions [#permalink] New post  15 Nov 2012, 08:35
vomhorizon wrote:
The diagonal of a square is approximately how much less than the two if its sides combined ?

(A) 30%
(B) 40%
(C) 29%
(D) 39%
(E) 66%


I think you meant "The diagonal of a square is approximately how much less than the two of its sides combined"

clearly, if side of a square is x , the diagonal will be \(x*\sqrt{2}\)
What we want is : \((2x-x*\sqrt{2} )*100/2x\) or \((2-\sqrt{2})*100/2\)

\(\sqrt{2}\) is approx 1.41 , therefore 100(2-1.41) is slightly less than 60. Dividing it by 2 we get a number slightly less than 30.
Among answer choices C is the only one slightly less than 30.

Ans C it is!
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Re: Collection of questions [#permalink] New post  15 Nov 2012, 08:36
Quote:
I think you meant "The diagonal of a square is approximately how much less than the two of its sides combined"


corrected !
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Re: Collection of questions [#permalink] New post  15 Nov 2012, 08:37
A square carpet with an area of 169m^2 must have 2 meters cut-off one of its edges in order to be a perfect fit for a rectangular room. What is the area of the rectangular room.?

(A) 140 m^2

(B) 128 m^2

(C) 143 m^2

(D) 147 m^2

(E) 151 m^2
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Re: Collection of questions [#permalink] New post  15 Nov 2012, 08:48
Of three numbers, the first is four times the second, and three times the third. If average of all the three numbers is 95, then the third number is?

(A) 57

(B) 76

(C) 38

(D) 60

(E) 130

Show Spoiler
Let the numbers be 12x, 3x, and 4x

The avg. of the numbers = 95; so 19x/3 = 95; x = 15

The third number is 4 x = 60 (D)

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Re: Collection of questions [#permalink] New post  Updated on: 16 Nov 2012, 03:00
If the average of a, b, c is M ad ab+bc = - ca then the average of a^2, b^2, c^2 is?

(A) M^2

(B) 3M^2

(C) 9M^2

(D) 36M^2

(E) 27M^2
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Originally posted by vomhorizon on 15 Nov 2012, 08:59.
Last edited by Bunuel on 16 Nov 2012, 03:00, edited 1 time in total.
Renamed the topic.
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Re: Collection of questions [#permalink] New post  15 Nov 2012, 09:07
A dealer marks articles at a price that gives him a profit of 30%. 6% of the consignment was lost in a fire, 24% was soiled and had to be sold at half the cost price. If the remainder was sold at the marked price, what percentage profit or loss did the dealer make on the consignment?

(A) 2%

(B) 2.5%

(C) 6.2%

(D) 3%

(E) He broke even ..
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Re: Collection of questions [#permalink] New post  15 Nov 2012, 09:07
First, you need to find the length of the sides of the original carpet:

x^2 = 169

x = 13

If you cut the length of the square by 2, the square now becomes a rectangle with the side lengths of: 13, 11, 13, 11.

New area of the carpet (and hence the room) is 13 x 11 = 143.

Not sure if this is a 700 level question.
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Re: Collection of questions [#permalink] New post  15 Nov 2012, 09:10
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vomhorizon wrote:
If the average of a, b, c is M ad ab+bc = - ca then the average of a^2, b^2, c^2 is?

(A) M^2

(B) 3M^2

(C) 9M^2

(D) 36M^2

(E) 27M^2


(a+b+c)/3 = M
=> a+b+c = 3M

ab + bc = -ca
=> ab+ bc+ca = 0

(a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca = a^2 + b^2 + c^2 + 2(ab + bc + ca)

substituting values
(3M)^2 = a^2 + b^2 + c^2 + 2*0
=> a^2 + b^2 + c^2 = 9M^2

Avg of a^2, b^2, c^2 = (a^2 + b^2 + c^2)/3 = (9M^2)/3 = 3M^2

So, Answer will be B
Hope it helps!
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Re: Collection of questions [#permalink] New post  15 Nov 2012, 09:26
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Of three numbers, the first is four times the second, and three times the third. If average of all the three numbers is 95, then the third number is?

(A) 57

(B) 76

(C) 38

(D) 60

(E) 130

F -> first, s-> second, t-> third
f = 4s
f = 3t

Let f be 12x then s = 3x and t = 4x
Avg = (12x+3x+4x)/3 = 95
=> x = 95*3/19 = 15

Third number = 4x = 4*15 = 60
So, Answer will be D
Hope it helps!
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Re: Collection of questions [#permalink] New post  15 Nov 2012, 09:35
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vomhorizon wrote:
A square carpet with an area of 169m^2 must have 2 meters cut-off one of its edges in order to be a perfect fit for a rectangular room. What is the area of the rectangular room.?

(A) 140 m^2

(B) 128 m^2

(C) 143 m^2

(D) 147 m^2

(E) 151 m^2


Side of the square is sqrt169 = 13m
since one of the side has to be reduced by 2m so the dimensions of the rectangle will be 13*11 = 143m^2
So, answer will be C. Hope it helps!
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Re: Collection of questions [#permalink] New post  15 Nov 2012, 09:41
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vomhorizon wrote:
A number when divided by 84 leaves a remainder of 57. What is the remainder when the same number is divided by 12?

(A) 7
(B) 8
(C) 9
(D) 11
(E) Cannot be determined


The number(n) can be written as
n = 84k + 57
where k is an integer

when n is divided by 12 then 84k+57 is divided by reminder.
84k goes with 12. and 57 gives 9 as a reminder when divided by 12.
So, 84k + 57 which is n will give 9 as reminder.

So, answer will be C
Hope it helps!
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Re: Collection of questions [#permalink] New post  15 Nov 2012, 10:05
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vomhorizon wrote:
A dealer marks articles at a price that gives him a profit of 30%. 6% of the consignment was lost in a fire, 24% was soiled and had to be sold at half the cost price. If the remainder was sold at the marked price, what percentage profit or loss did the dealer make on the consignment?

(A) 2%

(B) 2.5%

(C) 6.2%

(D) 3%

(E) He broke even ..


SP = 1.3 * CP (30% profit)
Total Size of the consignment is T
6% is lost so remaining is 94% of T
24% of T is sold at CP/2
Remaining 70% of T is sold at SP

Total SP = ((24/100) * T *CP/2) + ((70/100) * T * 1.3CP)
= T*CP (.12 + .91)
= T*CP (1.03)

So the profit is 3%

So, answer will be D
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Re: Collection of questions [#permalink] New post  15 Nov 2012, 10:11
vomhorizon wrote:
A dealer marks articles at a price that gives him a profit of 30%. 6% of the consignment was lost in a fire, 24% was soiled and had to be sold at half the cost price. If the remainder was sold at the marked price, what percentage profit or loss did the dealer make on the consignment?

(A) 2%

(B) 2.5%

(C) 6.2%

(D) 3%

(E) He broke even ..


If the original cost is x.
The money dealer made was = (6*0x + 24*0.5x+1.3x*70) /x %
= 12+91 = 103%

So the dealer made a profit of 3%

Ans D it is.
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Re: Collection of questions [#permalink] New post  15 Nov 2012, 10:50
I don't understand how it is 6.2%?!
Consider the consignment to be ‘y’.
If nothing went wrong he must have made money of 1.3xy
Since he sold 0.24y for x/2=> 0.12xy
0.06y is a loss
So the remaining is 0.7y which he sold for 0.7*1.3xy
Total money he made 0.12xy+0.91xy=1.03xy
Profit/Loss= (1.03xy-1.3xy)/1.3xy *100 = -0.27/1.3 *100 = 20% (approx loss)

Even if he is asking abt the profit he made on the amount he invested... the last line would be...
Profit/Loss= (1.03xy-xy)/xy *100 = 0.03*100 = 3% (approx profit)
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Re: Collection of questions [#permalink] New post  15 Nov 2012, 10:55
length of all sides = 13

now length of one side = 11

13*11=xx3. only one answer has 3 as the units digit. stop, there is your answer.
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Re: Collection of questions [#permalink] New post  15 Nov 2012, 20:04
We can also answer this question by simply plugging in..

Since the number leaves a remainder of 57 when divided by 84 , the number can be :

57 (Q is 0) , 141 (Q1 R57) , 225(Q2 R57), 309..... Etc

We can divide each one our "TEST NUMBERS" by 12, and we will get 9 as the remainder for each one..
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Re: Collection of questions [#permalink] New post  15 Nov 2012, 20:31
If a number can be divided by 84 and leaves a remainder of 57 . then it should be:
84x+57/12

Here x can be 0,1,2,3.....

So we got the number , 84x+57. Now divide this number by 12. Bingooooo 84 is divisible by 12 then only left is 57. Now divide 57/12.. we get 9..

This problem would be little more complicated if the divisor was 11.
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