If a number is to be randomly selected from set A above and a number

Question

GMAT CLUB'S FRESH CHALLENGE QUESTION:

A = {-10, -9, -8, -7, -6, -5, -4}
B = {-1/2, -1/3, -1/5, 0, 1/5, 1/3, 1/2}

If a number is to be randomly selected from set A above and a number is to be randomly selected from set B above, what is the probability that the product of the two numbers will be a negative integer?

A. 8/49
B. 12/49
C. 13/49
D. 18/49
E. 21/49

M37-59

Bunuel · Accepted Answer

Official Solution:

A = \{-10, \ -9, \ -8, \ -7, \ -6, \ -5, \ -4\} 
 
 B = \{-\frac{1}{2}, \ -\frac{1}{3}, \ -\frac{1}{5}, \ 0, \ \frac{1}{5}, \ \frac{1}{3}, \ \frac{1}{2}\} 
 
If a number is to be randomly selected from set A above and a number is to be randomly selected from set B above, what is the probability that the product of the two numbers will be a negative integer?

A.  \frac{8}{49} 
B.  \frac{12}{49} 
C.  \frac{13}{49} 
D.  \frac{18}{49} 
E.  \frac{21}{49}

For the product to be a negative  integer  the numbers chosen must have opposite signs and their product must result in an integer.
 
All number in A are negative, so from B we can only choose positive numbers.
 
If from B we choose  \frac{1}{5} , then from A we can choose -10 or -5. Two cases.
 
If from B we choose  \frac{1}{3} , then from A we can choose -9 or -6. Two cases.
 
If from B we choose  \frac{1}{2} , then from A we can choose -10, -8, -6, or -4. Four cases.
 
So, total of eight pairs will give a negative integer.
 
The total number of pairs is  7*7=49 , thus the probability is  \frac{8}{49} .

Answer: A

kablayi · Answer

I think answer is A

There are 7x7=49 possible products

And 8 oh them yield negative integers

1) -10x1/5
2) -10x1/2
3) -9x1/3
4) -8x1/2
5) -6x1/3
6) -6x1/2
7) -5x1/5
8) -4x1/2

Munch · Answer

A = {-10, -9, -8, -7, -6, -5, -4}
B = {-1/2, -1/3, -1/5, 0, 1/5, 1/3, 1/2}

If a number is to be randomly selected from set A above and a number is to be randomly selected from set B above, what is the probability that the product of the two numbers will be a negative integer?

A. 8/49
B. 12/49
C. 13/49
D. 18/49
E. 24/49 
--------------
Total number of ways is 7*7 =49

Number of ways to select 1 number from A --> 7C1 -->7
For the product to be negative select a positive number from B > no.of ways --> 3c1 -- >3

Total possibility -- > 7 *3 -- 21

Probability is 21/49

But i am not able to find the answer in the question stem

kablayi · Answer

]The question specifically asks for integers,

Munch · Answer

Oh ya!! thanks!! then it should be 8 .. I doubled checked the possibility to match the answer, but still missed the word integer..

merajul · Answer

A = {-10, -9, -8, -7, -6, -5, -4}
B = {-1/2, -1/3, -1/5, 0, 1/5, 1/3, 1/2}

I am not sure whether we should consider the product numbers of ‘0’.

Considering ‘0’ as an eligible possibility,
A X B will be -ve when, either A or B is -ve. Since all values for A is -ve, then all values of B must be +ve. In such case, only pairs will be -ve when value of B is 1/5 , 1/3 or 1/2. 
For each A, there will be 3 Negative Values, i.e
A X B = -10*1/5 = -10/5 ; -10/3 ; -10/2
 = -9/5 ; -9/3 ; -9/2
.
.
.
and so on.

Thus possible negative values will be = 7*3 =21

Total Possible product values will be = 7*7=49

Thus P(E) = 21/49. Option E is right.

yeshuverma · Answer

The question specifically asks for  -ve integers ("0" is not a -ve integer). Now Set A has only -ve integers so we have to select only +ve fractions from set B i.e.{1/5,1/3,1/2}.
With 1/5 we can only select -10 & -5 from set A. So possible combinations : 1/5*-10 & 1/5*-5. Number of possible combinations = 2

With 1/3 we can only select -9 & -6 from set A. Number of possible combinations = 2
With 1/2 we can only select -10,-8,-6,-4 from set A. Number of possible combinations = 4
Thus we have 2+2+4 = 8 combinations
Total Possible combinations = 7C1 * 7C1 = 49
Ans = 8/49

chetan2u · Answer

Since we are looking for negative integer, we have to consider only POSITIVE numbers in set B as all are NEGATIVE in set A..
1) 1/2
This will give integers when multiplied by MULTIPLE of 2
So -4,-6,-8,-10......4ways
2) 1/3
Similarly when multiplied by MULTIPLE of 3
-6,-9.....2ways
3) 1/5
When multiplied by MULTIPLE of 5
So -5,-10.....2ways

Total - 4+2+2=8ways
Possible products = 7*7=49

Ans 8/49

A

merajul · Answer

Bunuel · Answer

Par of  GMAT CLUB'S New Year's Quantitative Challenge Set

Kinshook · Answer

Total possibilities of AB = 7*7 = 49
Favorable possibilities of (A,B) = {(-10,1/5), (-10,1/2),(-9,1/3),(-8,1/2),(-6,1/3),(-6,1/2),(-5,1/5),(-4,1/2)} = 8

the probability that the product of the two numbers will be a negative integer = 8/49

IMO A

satya2029 · Answer

For negative INTEGER we have to only consider three positive numbers of set B as all the numbers of set A are negative. Since we are in search of an negative integer, it must be divisible by the number of other set.
For -10 we have 1/5 and 1/2 means (2 options)
For -9 only 1/3( 1 option)
For -7 No option
For -6 (2 options)
For -5(1 option)
For -4( 2 options)
Total options=8
one number from A 7c1 , and same for B 7c1
Total= 7c1*7c1=49
Required probability=8/49
A:)

exc4libur · Answer

Favorable outcomes: "negative integer"
{1/5} must be multiplied by a multiple of 5 to equal an integer: {-10,-5}=2
{1/3} must be multiplied by a multiple of 3 to equal an integer: {-9,-6}=2
{1/2} must be multiplied by a multiple of 2 to equal an integer: {-10,-8,-6,-4}=4

Total outcomes: 7C1•7C1=7•7=49 (ways to choose 1 from A and 1 from B)

P()=8/49

Ans (A)

If the question asked the probability of a negative number, then:
Favorable outcomes: 7C1•3C1=21
Total outcomes: 49
Probability: 21/49=3/7

A_Nishith · Answer

There are 7x7=49 possible products

And 8 oh them yield negative  integers

1) -10x1/5 
2) -10x1/2
3) -9x1/3
4) -8x1/2
5) -6x1/3
6) -6x1/2
7) -5x1/5
8) -4x1/2
Rest other multiples will give fraction or positive results.
So, total of eight pairs will give a negative integer.

Thus, the probability is  8/49

Answer: A

bumpbot · Answer

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If a number is to be randomly selected from set A above and a number

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