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The formula for the volume of a cylinder is:  Volume  =  pi · radius² · height

Entering the known values:                            392·pi  =  pi · radius² · height

Dividing both sides by pi:                                    392  =  radius² · 8

Dividing both sides by 8:                                       49  =  radius² 

Taking the square root of both sides:                      7  =  radius

Just a simple computer code in C++ and finds it in a flash.

Let there be d ducks and c cows.

you know that  d+c=24

It is reasonable to assume ever duck has 2 legs so that is 2d   duck leges

Also there would be 4c   cow legs

Total legs = 2d+4c = 66

so

d+c=24         (1)

2d+4c = 66   (2)

solve simultaneously.

2*4 is 8  and   2*2=4

half means divide by 2 and the opposite of divide is multiply.

Its C

Let No. of $2 gift packs = 16x

      No. of $5 gift packs = 9x

      No. of $10 gift packs = 7x

1/8 of $2 gift packs = 1/8 * 16x = 2x.

Total gift packs = 16x + 9x + 7x

                         = 32x

Total sold gift packs = 1/8 of $2 and 34 of $5

                                = (8x + 34)

     remaining gift packs = Total - Sold

                                      = 32x - (8x + 34)

                                      = (30x - 34)

Remaining gift packs -----> $2 ---> 14x

                                           $5 ---> 9x - 34

                                           $10 ---> 7x

        Value of $2 gift box = (14x * 2) = $28x

        Value of $5 gift box = 5(9x - 34) = $(45x - 170)

        Value of $10 gift box = 10(7x) = $70x

      Total remaining value = $(28x + 45x - 170 + 70x)

                     1975            = (143x - 170) dollars

                         2145 = 143x

                      => x = 15

   No. of $10 gift packs = 7x

                                     = 7 * 15

   No. of $10 gift packs = 105

You are not meant to use a calculator at all.

You are meant to understand how to do it.

The number out the front is an approximation of a surd (since it is a surd it cannot be expressed as a rational number.)

hint 

\(cos(3 \pi)+isin(3\pi)=e^{3\pi i}\)

Thanks  

Did you have a logical method or was it just trial and error?

Maybe you just had a computer check all the combinations for you?

=> Let assume the number of bags in shop (A) be x and in shop (B) be y

Now, According to question :-

        x = 180 + y ------ (1)

Also (180 + y) * 1/5 were transferred to shop (B)

So, y + (180 + y) * 1/5 = 24 + 4/5 (180 + y)

=> y + 36 + y/5 = 24 + 144 + 4/5y

=> y = y/5 - 4/5y = 144 + 24 - 36

v> 2/5y = 132 => y = 330

[Total No. of Bags in Shop (B) = 330]

You can picture these cities as all being on the same highway.

CC - YT - MT - LV

CC to YT = 37

YT to MT = 6

MT to LV = 8

This is a total of 51 miles, the same distance as from CC to LV.

This means that CC to MY is 43 miles.

233

also nice explanation here: https://gmatclub.com/forum/determine-the-largest-possible-integer-n-such-that-942-is-11190.html

use systems of equations

there are 5280 feet in a mile

-4 and -2

         n  d   q
1  = (4, 3, 0)
2  = (5, 0, 1)
3 = (3, 1, 1)
4 = (1, 2, 1)
5= (0, 0, 2)

y ==1/x^2 * k, where k==constant of proportionality

10 ==1/2^2 * k, solve for k

10 ==1/4 * k

k ==40

4000 ==1/x^2 * 40

4000/40 ==1/x^2100 ==
100 ==1/x^2, solve for x

x ==+or- 1/10

27/15 + 9/20 ==9 / 4

27 + 9 ==36 - sum of numerators in the LHS.

942! = 2^935 * 3^467 * 5^233 * 7^155 * 11^92 * 13^77 * 17^58 * 19^51 * 23^41 * 29^33 * 31^30 * 37^25 * 41^22 * 43^21 * 47^20 * 53^17 * 59^15 * 61^15 * 67^14 * 71^13 * 73^12 * 79^11 * 83^11 * 89^10 * 97^9 * 101^9 * 103^9 * 107^8 * 109^8 * 113^8 * 127^7 * 131^7 * 137^6 * 139^6 * 149^6 * 151^6 * 157^6 * 163^5 * 167^5 * 173^5 * 179^5 * 181^5 * 191^4 * 193^4 * 197^4 * 199^4 * 211^4 * 223^4 * 227^4 * 229^4 * 233^4 * 239^3 * 241^3 * 251^3 * 257^3 * 263^3 * 269^3 * 271^3 * 277^3 * 281^3 * 283^3 * 293^3 * 307^3 * 311^3 * 313^3 * 317^2 * 331^2 * 337^2 * 347^2 * 349^2 * 353^2 * 359^2 * 367^2 * 373^2 * 379^2 * 383^2 * 389^2 * 397^2 * 401^2 * 409^2 * 419^2 * 421^2 * 431^2 * 433^2 * 439^2 * 443^2 * 449^2 * 457^2 * 461^2 * 463^2 * 467^2 * 479 * 487 * 491 * 499 * 503 * 509 * 521 * 523 * 541 * 547 * 557 * 563 * 569 * 571 * 577 * 587 * 593 * 599 * 601 * 607 * 613 * 617 * 619 * 631 * 641 * 643 * 647 * 653 * 659 * 661 * 673 * 677 * 683 * 691 * 701 * 709 * 719 * 727 * 733 * 739 * 743 * 751 * 757 * 761 * 769 * 773 * 787 * 797 * 809 * 811 * 821 * 823 * 827 * 829 * 839 * 853 * 857 * 859 * 863 * 877 * 881 * 883 * 887 * 907 * 911 * 919 * 929 * 937 * 941

80= 2^4 * 5 - since the largest prime factor of 80 is 5 and 5 above has an exponent of 233, therefore the largest n =233. Or: 942! mod 80^233=0

The first term is 7/64.

The smallest possible value of A + B + C + D is 33.

\(\log_2 (x) = 61\)

Let the price of the item==$100

100 x (1 - 0.12) ==$88.00

88  x  (1 - 0.06)==$82.72 - final discount price

100 - 82.72 ==17.28% percentage of total discount.

60  x  30/60 ==30 miles - distance covered in the first 30 minutes.

65  x  30/60 ==32.5 miles - distance covered in the 2nd 30 minutes.

96 - 30 - 32.50 ==33.50 miles - distance covered in the last 30 minutes.

33.50 / (30/60) ==33.50  x  60/30 ==67 mph - his average speed for the last 30 minutes.

Average speed ==Total distance / total time.

16  x  30/60 ==15 miles travelled on bicycle

4  x  90/60 == 6 miles covered by walking

15  +  6 ==21 miles - total distance travelled.

30/60  +  90/60 ==2 hours - total time

21 / 2 ==10.50 mph - here average speed for the entire trip.

Let the entire distance be 3x

Normally that takes 180 minutes

speed would be  (3x)/180  =  x/60   miles per minute

--------------

Storm day

It would take 60 minutes to go the first distance of x

then

276-60 = 216 minutes to go the next leg of 2x

speed is   \(\frac{x}{60}-\frac{20}{60}=\frac{x-20}{60}\;miles\; per \;minute\)

speed = distance /time

\(\frac{x-20}{60}=\frac{2x}{216}\\ \frac{x-20}{60}=\frac{2x}{27*8}\\ \frac{x-20}{10}=\frac{x}{18}\\ 18x-360=10x\\ 8x=360\\ x=45 miles\\ Total \;\;distance = 3*45 = 135miles.\)