GMAT Problem Solving Discussions

MBA
2701
couple of crispy ones:

A cube of side 5cm is painted on all its side. If it is sliced into 1 cubic centimer cubes, how many 1 cubic centimeter cubes will have exactly one of their sides painted?
A. 9
B. 61
C. 98
D. 54
E. 64



IMO Ans D ...

Inner 3*3 square i.e 9 cubes on each of the 6 outer faces...

Hence total 9*6 = 54 cubes

Too sleepy ..may have missed out a few cubes ...2nd one tomm ...
2702

below are OAs. Kudos to Vikram and Bhavin!!
1. D
2. A

couple of crispy ones:

A cube of side 5cm is painted on all its side. If it is sliced into 1 cubic centimer cubes, how many 1 cubic centimeter cubes will have exactly one of their sides painted?
A. 9
B. 61
C. 98
D. 54
E. 64

A lady grows cabbages in her garden that is in the shape of a square. Each cabbage takes 1 square feet of area in her garden. This year, she has increased her output by 211 cabbages as compared to last year. The shape of the area used for growing the cabbages has remained a square in both these years. How many cabbages did she produce this year?
A. 11236
B. 11025
C. 14400
D. 12696
E. Cannot be determined
2703

guys, need your help on below:

1. what is the result of adding the units digit of 2002^2002 and 7007^7007

a. 1
b. 4
c. 5
d. 7
e. 9

this one is from Kaplan monthly quiz "Yellow".

2704
guys, need your help on below:

1. what is the result of adding the units digit of 2002^2002 and 7007^7007

a. 1
b. 4
c. 5
d. 7
e. 9

this one is from Kaplan monthly quiz "Yellow".


the solution needs to find the last digit of the two expression.Cyclicity concept wii be beneficial here.
cyclicity of 2 is-4 and cyclicity of 7 is also 4.
so the last digit of
2002^2002=(2000+2)^(4*500+2)=2^2000*2^2=6*4=4
similiarly for 7=>3
so last digit is 3+4=7
2705
guys, need your help on below:

1. what is the result of adding the units digit of 2002^2002 and 7007^7007

a. 1
b. 4
c. 5
d. 7
e. 9

this one is from Kaplan monthly quiz "Yellow".

simpul it is
cyclicity of 2 is 4 and cyclicity of 7 is also 4
remainder of 2002/4=2
remainder of 7007/4=3

now 2 pow 2=last digit is 4
and 7 pow 3=last digit is 3
summation is 4+3=7
2706
couple of crispy ones:

A cube of side 5cm is painted on all its side. If it is sliced into 1 cubic centimer cubes, how many 1 cubic centimeter cubes will have exactly one of their sides painted?
A. 9
B. 61
C. 98
D. 54
E. 64


a simple formula for finding the no. of cubes..
Let n= number to be cubed
No. of small cubes with 0 face colored = (n-2)^3
No. of small cubes with 3 faces colored=8
No. of small cubes with 2 faces colored=12(n-2)
No. of small cubes with 1 faces colored=6(n-2)^2

here n=5
No. of small cubes with 1 faces colored=6(n-2)^2=6(3)^2=54
2707
simpul it is
cyclicity of 2 is 4 and cyclicity of 7 is also 4
remainder of 2002/4=2
remainder of 7007/4=3

now 2 pow 2=last digit is 4
and 7 pow 3=last digit is 3
summation is 4+3=7

sowie.. i din't catch the cyclicity & remainder ka funda.. could you please explain!!
2708

sowie.. i din't catch the cyclicity & remainder ka funda.. could you please explain!!


cyclicity .... the units digit starts repeating ...

2^1 =2
2^2=4
2^3=8
2^4=16
----------------------now it will repeat...after 4 attempts..hence cyclicity 4
2^5=32
2^6=64 .....same way you could try for other single digit nos.

2709

The sum of all the digits of the positive integer q is equal to 3 didgit numbers X13. if Q = 10^N - 49, what is the value of N?

2710
amsey1382 Says
The sum of all the digits of the positive integer q is equal to 3 didgit numbers X13. if Q = 10^N - 49, what is the value of N?



Is N = 25??
2711
amsey1382 Says
The sum of all the digits of the positive integer q is equal to 3 didgit numbers X13. if Q = 10^N - 49, what is the value of N?


OA is 25...:drinking:
2712
amsey1382 Says
The sum of all the digits of the positive integer q is equal to 3 didgit numbers X13. if Q = 10^N - 49, what is the value of N?

Cool!! :)
What i did ->
1000 - 49 = 951.. so all we need to is figure out is how many 9s!!
We know that the sum is "X13" .. so we start with 113...

5 + 1 + 9x = 113... dint work, x is not an integer
5 + 1 + 9x = 213 .... x = 23

thus, 23 + 2 (for 51) = 25!!
2713

Plz provide your explanation too.

What range of values of x will satisfy the inequality 2x + 3 > 7x - 2?
A. x 5
B. -1 C. (-1/9) D. (-1/9) E. x 1

2714
amsey1382 Says
The sum of all the digits of the positive integer q is equal to 3 didgit numbers X13. if Q = 10^N - 49, what is the value of N?

Cool!! :)
What i did ->
1000 - 49 = 951.. so all we need to is figure out is how many 9s!!
We know that the sum is "X13" .. so we start with 113...

5 + 1 + 9x = 113... dint work, x is not an integer
5 + 1 + 9x = 213 .... x = 23

thus, 23 + 2 (for 51) = 25!!


I concur ...Ans should be 25 ...

Q = 10^n - 49 ...Hence it is of the kind 9999999......(n-2 times)51

Hence sum of digits of Q is (n-2)9 + 5 + 1 = X13

i.e (n-2)9 = X13-6
i.e (n-2)9 = X07
Now X07 has to be a multiple of 9 ...hence X = 2
and, (n-2)9 = 207

Hence, n=25
2715
Plz provide your explanation too.

What range of values of x will satisfy the inequality 2x + 3 > 7x - 2?
A. x 5
B. -1 C. (-1/9) D. (-1/9) E. x 1


Solved hastily ..is the ans C ?
2716
bhavin422 Says
Solved hastily ..is the ans C ?

What range of values of x will satisfy the inequality 2x + 3 > |7x - 2?
A. x 5
B. -1 C. (-1/9) D. (-1/9) E. x 1


It cant be C, coz it says x>(-1/9)

Lets say x is -> (-1/2)
then 2x + 3| = |-1 + 3 = 2
7x - 2| = |-3.5-2| = -5.5 = 5.5 which is greater than 2.

I'm unable to solve.. 😞
2717

ans is C. Bhavin please explain Man. Such problems whack me.


ndhadha,
u incorrectly assumed -1/2 as > -1/9

It cant be C, coz it says x>(-1/9)

Lets say x is -> (-1/2)
then 2x + 3 = |-1 + 3 = 2
7x - 2| = |-3.5-2| = -5.5 = 5.5 which is greater than 2.

I'm unable to solve.. :(
2718
It cant be C, coz it says x>(-1/9)

Lets say x is -> (-1/2)
then 2x + 3 = |-1 + 3 = 2
7x - 2| = |-3.5-2| = -5.5 = 5.5 which is greater than 2.

I'm unable to solve.. :(


Hello nisha ..incorrect assumption for x since -1/2 is not greater than -1/9
Ans has to be C ..

Explanation :
When u get rid of absolutes associate + and - sign ..
Hence, 4 poss .
2x+3 > 7x-2 x
2x+3> -(7x-2 ) x>-1/9
-(2x+3) > 7x-2 x
-(2x+3) > -(7x-2 ) x>1
From 4 boundary values, identify lower and upper cut off
Hence, lower cut off is -1/9 and upper cut off is 1
So, -1/9
2719
ans is C. Bhavin please explain Man. Such problems whack me.


ndhadha,
u incorrectly assumed -1/2 as > -1/9



damn!! silly mistakes will kill me!!

Good job, Bhavin - u were sleepy n u did that!! 😃
2720

double post