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# Together Ari and Izy have less than P colored markers. Ari has P - 2

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Together Ari and Izy have less than P colored markers. Ari has P - 2  [#permalink]

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21 Apr 2018, 10:17
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81% (01:28) correct 19% (01:59) wrong based on 63 sessions

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Together Ari and Izy have less than P colored markers. Ari has P - 2 colored markers and Izy has P - 20 colored markers. If each girl has at least one colored marker, what is the value of P?

(A) 21
(B) 22
(C) 22
(D) 24
(E) 25

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Re: Together Ari and Izy have less than P colored markers. Ari has P - 2  [#permalink]

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21 Apr 2018, 10:36
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Together Ari and Izy have less than P colored markers. Ari has P - 2 colored markers and Izy has P - 20 colored markers. If each girl has at least one colored marker, what is the value of P?

Lets try to find solution by direct substitution and elimination method

Constraints:
1. Number of colored markers of both girls should not exceed P
2. Ari and Izy should have atleast 1 colored marker

Step 1:
The constraint 2 eliminates answers B and C , if P is 22 , then Ari will have 20 (22-2) and Izy will have 2 (22-20). So total markers is 22 which is equal to P. so B and C eliminated.

Step 2:
Lets consider P as 24 , then Ari = 22 (24-2) and Izy = 4 (24-20) , total 26 which is higher than P. We can eliminate Choice D. We can eliminate option E as well.

We are left with option A.

We can confirm that A is right answer just in case. P = 21 , Ari = 19 (21-2) and Izy = 1 (21-20). Total 20 < P.

Ans: A
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Together Ari and Izy have less than P colored markers. Ari has P - 2  [#permalink]

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21 Apr 2018, 11:01
1
Bunuel wrote:
Together Ari and Izy have less than P colored markers. Ari has P - 2 colored markers and Izy has P - 20 colored markers. If each girl has at least one colored marker, what is the value of P?

(A) 21
(B) 22
(C) 22
(D) 24
(E) 25

I looked at this problem three times. I could not understand the question. As inline text, I did not see P - 2 and P - 20 as (P - 2) and (P - 20) until akadiyan posted. +1

Ari, A = (P - 2) markers
Izy, I = (P - 20) markers

Together, they have fewer than P markers.
Each girl has at least one marker.

$$A + I < P$$
$$(P - 2) + (P - 20) < P$$
$$P - 2 + P - 20 < P$$
$$2P - 22 < P$$
$$P < 22$$

Only one answer, A, is < 22
P = 21

You could stop here.
If not sure, check answers A and B.

A) 21. If P = 21, Ari = 19 and Izy = 1. Together = 20
20 < 21. That works.

B) 22. P cannot be 22. Ari = 20 and Izy = 2. Together they would have 22. Not allowed*

P must = 21

*Greater than 22? No. The girls' total will exceed P by greater and greater numbers.
The absolute value of the girls' combined integer difference is 22: (-2 + (-20)) = (-2 - 20) = -22, |-22| = 22
After P = 22, the girls' total will exceed that absolute value of combined difference (22), by +2, +4, +6.
If P = 23: A = 21, I = 3, both = 24 (= 22 + 2). 24 > 23. Not allowed. If P = 24, together = 26 ( = 22 + 4).

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Re: Together Ari and Izy have less than P colored markers. Ari has P - 2  [#permalink]

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22 Apr 2018, 01:01
Bunuel wrote:
Together Ari and Izy have less than P colored markers. Ari has P - 2 colored markers and Izy has P - 20 colored markers. If each girl has at least one colored marker, what is the value of P?

(A) 21
(B) 22
(C) 22
(D) 24
(E) 25

Ari and Izy have less than P

i,e, A + I < P

Ari has P - 2 colored markers

i.e. A = (P-2)

Izy has P - 20 colored markers

i.e. I = (P-20)

Each has atleast one colored Marker

i.e. (P-20) > 0 i.e. P > 20

Now, A + I < P

i.e. (P-2) + (P-20) < P

i.e. P < 22

Hence P = 21

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Re: Together Ari and Izy have less than P colored markers. Ari has P - 2 &nbs [#permalink] 22 Apr 2018, 01:01
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