GMAT Problem Solving Discussions

Here's another one.. plz help!

In a game of chess, the moves of white and black pieces alternate, with white pieces having the first move. During a certain chess tournament, the white pieces have made 2319 moves altogether, while the black pieces have made a total of 2315 moves. In every game, either the white side wins, black side wins, or there is a draw. If it is impossible for the losing side to make the last move in a game, which of the following could be true about the tournament?

1) the black sides lost 5 games
2) the black sides won more games than the white sides.
3) all games ended in a draw.

A) 3 only
B) 1 & 2 only
C) 1 & 3 only
D) 2 & 3 only
E) 1, 2, & 3.


As per me the answer should be A, is that the OA ??
In ur solution u r considering only the condition x,y,z, are +ve only.......x,y,z can be
-ve also making equation greater than zero.......

dear ashish,

if u plug in some values for x,y and z, u vil notice tht all 3 must be +ve for equations to be consistent.

Answer is (D).

I went for (A) too!.. Can someone plz explain?

Dopa Says
As per me the answer should be A, is that the OA ??

The right Answer is (D) -> 2 & 3.

holy_luv Says
ans should be option A...let me kno if dat's correct
dear ashish,

if u plug in some values for x,y and z, u vil notice tht all 3 must be +ve for equations to be consistent.

consider when x,y,z are -1,-2,-3

here x(y+z) is greater than zero. ie x,y,z is not necesserily +ve.......this is what i mean.......
consider when x,y,z are -1,-2,-3

here x(y+z) is greater than zero. ie x,y,z is not necesserily +ve.......this is what i mean.......

yup u r right.....all -ve values of x, y and z also work out.
either eachof x,yz shud be +e or -ve else the statements alone wud nt be suff

hence OA wud still be C

thnz ashish for providing an alternative.

Q. How many integers between 0 and 1560 have a prime tens digit and a prime units digit.

A) 295
B) 252 (OA)
C) 236
D) 96
E) 76

Can someone please explain how to solve this question without actual manual counting?

Regards
MSD

Ratio Problem
Foodmart customers regularly buy at least one of the following products:
milk
, chicken,or apples.60%of shoppers buy milk,50% buy chicken,and35% buy apples.If10%of the customers buy all3 products, what percentage of Foodmart customers purchase 2of the above products? :sarcasm:

A)5%
B)10%
C)15%
D)25%
E)30%
OA : C

I think the Answer should be (D) = 25 %

Can you cross-check?

Ratio Problem

Foodmart customers regularly buy
at least one of the following products:
milk
, chicken,or apples.60%of shoppers buy milk,50% buy chicken,and35% buy apples.If10%of the customers buy all3 products, what percentage of Foodmart customers purchase 2of the above products? :sarcasm:

A)5%
B)10%
C)15%
D)25%
E)30%
OA : C

The prime numbers that can be used to fill the tens and units digit are 2,3,5 & 7.

The numbers that can be formed between 0 to 1560 can be found as follows:-

2-digit nos. --> 4*4 = 16
3-digit nos. --> 9*4*4 = 144
4-digit nos between 1000 - 1499 --> 1*5*4*4 = 80
4-digit nos between 1500 - 1559 --> 1*1*3*4 = 12

Summing them up --> 16 + 144 + 80 + 12 = 252.

Hope this helps!

Q. How many integers between 0 and 1560 have a prime tens digit and a prime units digit.

A) 295
B) 252 (OA)
C) 236
D) 96
E) 76

Can someone please explain how to solve this question without actual manual counting?

Regards
MSD
Ratio Problem
Foodmart customers regularly buy at least one of the following products:
milk
, chicken,or apples.60%of shoppers buy milk,50% buy chicken,and35% buy apples.If10%of the customers buy all3 products, what percentage of Foodmart customers purchase 2of the above products? :sarcasm:

A)5%
B)10%
C)15%
D)25%
E)30%
OA : C


I am getiing d as answer can u check it please

see

n(AUBUC)= n(A)+n(B)+n(C)-((nA@B)+(nA@BC)+(nC@B))+(nA@B@C) where @ denotes intersection

using this we get the answer of ((nA@B)+(nA@BC)+(nC@B)) as 55 and substracting the 30 (10+10+10) from it as we need to find only the numbers of customers who purchase 2 of the items hence 25%

also the venn diagram gives the same result...
I am getiing d as answer can u check it please

see

n(AUBUC)= n(A)+n(B)+n(C)-((nA@B)+(nA@BC)+(nC@B))+(nA@B@C) where @ denotes intersection

using this we get the answer of ((nA@B)+(nA@BC)+(nC@B)) as 55 and substracting the 30 (10+10+10) from it as we need to find only the numbers of customers who purchase 2 of the items hence 25%

also the venn diagram gives the same result...

25 for me too...
Q. How many integers between 0 and 1560 have a prime tens digit and a prime units digit.

A) 295
B) 252 (OA)
C) 236
D) 96
E) 76

Can someone please explain how to solve this question without actual manual counting?

Regards
MSD

hmm...counting takes time??...guess it's a minute affair..
jus find such nos. from 1 to 100 which coms to 16....
extend it upto 1600 as 16*16 = 256 and subtract all such nos... >1560 and anser->252
I am getiing d as answer can u check it please

see

n(AUBUC)= n(A)+n(B)+n(C)-((nA@B)+(nA@BC)+(nC@B))+(nA@B@C) where @ denotes intersection

using this we get the answer of ((nA@B)+(nA@BC)+(nC@B)) as 55 and substracting the 30 (10+10+10) from it as we need to find only the numbers of customers who purchase 2 of the items hence 25%

also the venn diagram gives the same result...


Well even I was getting D as the answer so i think the OA is misprinted.
Ratio Problem
Foodmart customers regularly buy at least one of the following products:
milk, chicken,or apples.60%of shoppers buy milk,50% buy chicken,and35% buy apples.If10%of the customers buy all3 products, what percentage of Foodmart customers purchase 2of the above products? :sarcasm:
A)5%
B)10%
C)15%
D)25%
E)30%
OA : C


Well, the answer should be C. Let me explain.....
Here, we've been asked the percentage of customers who purchased exactly 2 of the products. So we dont need to count those who purchased all three products.
Hence, 60 + 50 + 35 - 3(10) = 145 - 30 = 115
Therefore 15% is the answer.
If the question would have been ... what is the percentage of customers who purchased 2 or more products...then we would have subtracted 2(10) i.e 20 and then the answer would have been 25%. Any views?

Regards
MSD
Well, the answer should be C. Let me explain.....
Here, we've been asked the percentage of customers who purchased exactly 2 of the products. So we dont need to count those who purchased all three products.
Hence, 60 + 50 + 35 - 3(10) = 145 - 30 = 115
Therefore 15% is the answer.
If the question would have been ... what is the percentage of customers who purchased 2 or more products...then we would have subtracted 2(10) i.e 20 and then the answer would have been 25%. Any views?

Regards
MSD

I think this approach is not correct.
when you say no. of people buying exactly two, you calculate it as
60 + 50 + 35 -3(10) - ALL
here you put ALL as 100 but actually it should be 90.
I guess a Venn Diagram makes it clearer.
*arch* Says
The right Answer is (D) -> 2 & 3.

Hi arch,
can you please tell how u reached this answer
Well, the answer should be C. Let me explain.....
Here, we've been asked the percentage of customers who purchased exactly 2 of the products. So we dont need to count those who purchased all three products.
Hence, 60 + 50 + 35 - 3(10) = 145 - 30 = 115
Therefore 15% is the answer.
If the question would have been ... what is the percentage of customers who purchased 2 or more products...then we would have subtracted 2(10) i.e 20 and then the answer would have been 25%. Any views?

Regards
MSD

Let milk, chicken and aples be represented by M, C and A respectively.
Given n(M)=0.25x, n(C)=0.5x, n(A)=0.35x
Given percentage of shoppers who buy all 3 items is 0.1x, where x represents total size of shoppers
Let a,b and c represent %age who buy both milk and chocolate, milk and apples and and chicken and apples respectively.
Only milk = 0.5x-(a+b)
Only chicken= 0.4x-(a+c)
Only apples= 0.25x-(b+c)
Adding up all
1.15x-2(a+b+c)+(a+b+c)+0.1x=x
hence (a+b+c)=0.25x

OA=25%


Regards
Let milk, chicken and aples be represented by M, C and A respectively.
Given n(M)=0.25x, n(C)=0.5x, n(A)=0.35x
Given percentage of shoppers who buy all 3 items is 0.1x, where x represents total size of shoppers
Let a,b and c represent %age who buy both milk and chocolate, milk and apples and and chicken and apples respectively.
Only milk = 0.5x-(a+b)
Only chicken= 0.4x-(a+c)
Only apples= 0.25x-(b+c)
Adding up all
1.15x-2(a+b+c)+(a+b+c)+0.1x=x
hence (a+b+c)=0.25x

OA=25%


Regards

in continuation to my above post, the ques here imlies"how many shoppers buy exactly 2 of the 3 products" which is 25%

had the ques been "how many shoppers buy at least 2 products" it wud be 35%

Here's the answer explanation..

Hi arch,
can you please tell how u reached this answer