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Difficulty:
15%
(low)
Question Stats:
82% (01:22) correct
18%
(01:39)
wrong
based on 106
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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) 23
(D) 24
(E) 25
(A) 21
(B) 22
(C) 23
(D) 24
(E) 25
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
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
21 Apr 2018, 11:01
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Bunuel
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
Answer A
*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).
