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# A certain number of people wait in line at a bank until served. How ma

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Math Expert
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A certain number of people wait in line at a bank until served. How ma  [#permalink]

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13 Nov 2019, 23:42
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69% (01:36) correct 31% (01:14) wrong based on 51 sessions

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A certain number of people wait in line at a bank until served. How many people are presently in line?

(1) If 2 more people joined the line and none of those currently waiting were served, there would be at least 10 people waiting in line.

(2) If no more people joined the line and 4 of the people currently waiting were served, there would be fewer than 5 people waiting in line.

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Re: A certain number of people wait in line at a bank until served. How ma  [#permalink]

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14 Nov 2019, 00:16
1
(1) If 2 more people joined the line and none of those currently waiting were served, there would be at least 10 people waiting in line.
--> Possible Number of people currently waiting = {8, 9, 10, . . . . . . } --> Insufficient

(2) If no more people joined the line and 4 of the people currently waiting were served, there would be fewer than 5 people waiting in line
--> Possible Number of people currently waiting = {8, 7, 6, 5, 4} --> Insufficient

Combining (1) & (2),
Possible number = 8 ONLY --> Sufficient

IMO Option C
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Re: A certain number of people wait in line at a bank until served. How ma  [#permalink]

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14 Nov 2019, 00:21
1
Bunuel wrote:
A certain number of people wait in line at a bank until served. How many people are presently in line?

(1) If 2 more people joined the line and none of those currently waiting were served, there would be at least 10 people waiting in line.

(2) If no more people joined the line and 4 of the people currently waiting were served, there would be fewer than 5 people waiting in line.

(1) - Tells us that the number of people in the line must be $$\geq$$8, so there could be 8 or 9 or 10 etc people in the line INSUFF.
(2)- Tells us that the number of people in the line must be $$\leq$$ 8, so there could be , 8 or 7 or 6 etc people in the line INSUFF.

1+2

From (1) number of people cannot be less than 8 from (2) number of people cannot be more than 8 , hence number of people must be 8, SUFF.

Ans- C
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Re: A certain number of people wait in line at a bank until served. How ma  [#permalink]

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14 Nov 2019, 01:53
A certain number of people wait in line at a bank until served. How many people are presently in line?
Let there are 'x' people presently in the line.

(1) If 2 more people joined the line and none of those currently waiting were served, there would be at least 10 people waiting in line.
Here, total people in line after 2 join them = x + 2
Sine no one was served x + 2 = 10
x = 8

SUFFICIENT.

(2) If no more people joined the line and 4 of the people currently waiting were served, there would be fewer than 5 people waiting in line.
Here, total people after 4 were served = x - 4
As per statement possibilities are:
x - 4 = 1 => x = 5
x - 4 = 2 => x = 6
x - 4 = 3 => x = 7
x - 4 = 4 => x = 8

INSUFFICIENT.

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Re: A certain number of people wait in line at a bank until served. How ma  [#permalink]

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14 Nov 2019, 03:16
1
Quote:
A certain number of people wait in line at a bank until served. How many people are presently in line?

(1) If 2 more people joined the line and none of those currently waiting were served, there would be at least 10 people waiting in line.
(2) If no more people joined the line and 4 of the people currently waiting were served, there would be fewer than 5 people waiting in line.

(1) If 2 more people joined the line and none of those currently waiting were served, there would be at least 10 people waiting in line. insufic

w+2≥10, w≥8

(2) If no more people joined the line and 4 of the people currently waiting were served, there would be fewer than 5 people waiting in line. insufic

0<w-4<5, 0<w<9

(1 & 2) sufic

w≥8 and 0<w<9, w=8

Ans (C)
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Re: A certain number of people wait in line at a bank until served. How ma  [#permalink]

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14 Nov 2019, 04:03
1
(1) If 2 more people joined the line and none of those currently waiting were served, there would be at least 10 people waiting in line.

Then the no.of before can be 8,9,10.......
Insufficient

(2) If no more people joined the line and 4 of the people currently waiting were served, there would be fewer than 5 people waiting in line.

So, no.of people before leaving can be 8,7,6.....

Insufficient

Combining both we get the no.of people are 8....

Sufficient

OA:C

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Re: A certain number of people wait in line at a bank until served. How ma  [#permalink]

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14 Nov 2019, 06:12
1
let total people in line = x
#1
If 2 more people joined the line and none of those currently waiting were served, there would be at least 10 people waiting in line.
x+2>=10
x>=8
insufficient
#2
If no more people joined the line and 4 of the people currently waiting were served, there would be fewer than 5 people waiting in line
x-4<5
x<9
insufficient
from 1&2
we can say that x=8
IMO C

A certain number of people wait in line at a bank until served. How many people are presently in line?

(1) If 2 more people joined the line and none of those currently waiting were served, there would be at least 10 people waiting in line.

(2) If no more people joined the line and 4 of the people currently waiting were served, there would be fewer than 5 people waiting in line.
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Re: A certain number of people wait in line at a bank until served. How ma  [#permalink]

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14 Nov 2019, 10:14
1
A certain number of people wait in line at a bank until served. How many people are presently in line?
Total = x ?
(1) If 2 more people joined the line and none of those currently waiting were served, there would be at least 10 people waiting in line.
x+2 = 10, x = 8
x+2 = 11, x = 9, X>8 Insufficient.

(2) If no more people joined the line and 4 of the people currently waiting were served, there would be fewer than 5 people waiting in line.
X - 4 =4 , x = 8
x-4 = 3, x=7 , X<8 Insufficient.
1) + 2) x can be 8 only
Sufficient.

Imo. C
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Re: A certain number of people wait in line at a bank until served. How ma  [#permalink]

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14 Nov 2019, 11:05
(1) If 2 more people joined the line and none of those currently waiting were served, there would be at least 10 people waiting in line.

If 2 joined, there would be 10. Therefore currently 8 are in the line. Sufficient.

(2) If no more people joined the line and 4 of the people currently waiting were served, there would be fewer than 5 people waiting in line.

fewer than 5 people could mean 4,5,6,7 and 8 are currently waiting. Insufficient.

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Re: A certain number of people wait in line at a bank until served. How ma  [#permalink]

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14 Nov 2019, 11:34
1
Let x be the no. of people. We have to find x.

(1) x+2 ≥ 10, x ≥ 8. NOT SUFFICIENT
(2) x-4 < 5, x < 9. NOT SUFFICIENT
(1) & (2) x must be interger, as number of people. ∴ x=8. SUFFICIENT

Ans: C
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Posts: 788
Re: A certain number of people wait in line at a bank until served. How ma  [#permalink]

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14 Nov 2019, 12:29
2
We are to determine the number of people presently in line to be served at the bank.

Let x be the number of people currently in the queue in the bank.

Statement 1: If 2 more people joined the line and none of those currently waiting were served, there would be at least 10 people waiting in line.
x+2 ≥ 10
this implies x≥8
Not sufficient since we can have 8, 9, 10, and many other possibilities of people waiting in line to be served.

Statement 2: If no more people joined the line and 4 of the people currently waiting were served, there would be fewer than 5 people waiting in line.
x-4 < 5
x<9
Not sufficient since the number of people waiting in line can be 8, 7, or 6. Statement does not lead to a unique value of x.

1+2
x≥8 and x<9
from the above, we are able to conclusively say that x=8.
Hence, both statements taken together is sufficient.

Re: A certain number of people wait in line at a bank until served. How ma   [#permalink] 14 Nov 2019, 12:29
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