GMAT Club Around The World!!! How many integers that have a value less

Question

How many integers that have a value less than 4 satisfy the inequality  (y+1)(y+2)(y+4) \geq 0 ?

A. 4
B. 5
C. 6
D. 7
E. 8

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Deepakjhamb · Answer

How many integers that have a value less than 4 satisfy the inequality (y+1)(y+2)(y+4)≥0(y+1)(y+2)(y+4)≥0?

A. 4
B. 5
C. 6
D. 7
E. 8

now we get -4 <=y <= -2 and y >= -1 and also y < 4

so we have solutions as -4,-3 ,-2 ,-1 ,0,1,2,3 so total 8 integers satisfy eq < 4

so answer is e) 8

BIDJI23 · Answer

Let's see : when this condition is <0?

When only the 3 factors are under 0.

When 2 factors are <0 and one above 0, then the condition is >=0

When the first factor is under 0, the second one is equal to 0... So we can not have 1 negative factor and 2 positive.

Then when the 3 factors are under 0 ? When y<-4

So let's count for our problem here: -4;-3;-2;-1;0;1;2;3

PUSH E

ananya3 · Answer

IMO E

values of y = {-4,-2,-1}
case 0: for the above values (y+1)(y+2)(y+4) = 0

case 1:
y < -4
(y+1)(y+2)(y+4)< 0

case 2:
-4 <= y <-2
(y+1)(y+2)(y+4) >= 0

case3:
-2 <= y <-1
(y+1)(y+2)(y+4) <= 0

case 4:
y>= -1
(y+1)(y+2)(y+4) >= 0

possible values of y less than 4 that satisfy the inequality (y+1)(y+2)(y+4) >= 0 are: {-4,-3,-2,-1,0,1,2,3}
number of integers = 8

Attachments

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rocky620 · Answer

Kindly refer the image below:

There will be three nodes: -4,-2,-1
Since it is greater than or equal to we will take the values in positive sections along with the nodal values.

Between -2 & -4 = 3 values (-2, -3, -4)
Between 4 & -1 = 5 values (-1, 0, 1, 2, 3) we cannot include 4 as the values need to be less than 4.

Total 8 integral values.

IMO Option E

TarunKumar1234 · Answer

Given expression, (y+1)(y+2)(y+4)≥0 So, y = U So, I think E.

Green2k1 · Answer

Correct Answer E

How many integers that have a value less than 4 satisfy the inequality (y+1)(y+2)(y+4)≥0?

will be equal to 0 at -1, -2, -4. after drawing on the number line, possible acceptable values are
3, 2, 1, 0, -1, -2, -3 ,-4

Total = 8

manasi05 · Answer

(y+1) (y+2) (y+4) >=0
After plotting the values on number line we will get the range of y
y >= -1
-4 <= y <= -2
So the integers that have a value less then 4 which satisfy the inequality will be
-4, -3, -2, -1, 0, 1, 2, 3
So there will be total 8 integer values

So the answer will be E

Talha95 · Answer

We can find the values which satisfy the equation are 0,1,2,3,-1,-2,-3,-4=8 .
Ans: E.

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CEdward · Answer

How many integers that have a value less than 4 satisfy the inequality (y+1)(y+2)(y+4)≥0

A. 4
B. 5
C. 6
D. 7
E. 8

The question is asking, for how many integers where y < 4 is the inequality satisfied.

Let's pick the numbers in descending order: 
3 YES
2 YES
1 YES 
0 YES
-1 YES
-2 YES
-3 YES
-4 YES
-5 NO

Anything less than -4 is out. I count 8 YES.

Answer is E

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GMAT Club Around The World!!! How many integers that have a value less

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GMAT Club Around The World!!! How many integers that have a value less

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