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29 May 2023, 12:43
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Difficulty:
95%
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Question Stats:
33% (02:39) correct
67%
(02:40)
wrong
based on 33
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Deepti has 49 stamps which are of one-rupee. 50 paise and 25 paise denominations. The total value of her stamps is 23.50. If the number of 25 paise stamps is greater than the number of 50 paise stamps and one-rupee stamps together, and the number of one-rupee stamps is less than 50 paise stamps, how many more 25 paise stamps than one-rupee stamps does Deepti have?
(A) 15
(B) 14
(C) 1
(D) 26
(E) 25
Posted from my mobile device
(A) 15
(B) 14
(C) 1
(D) 26
(E) 25
Posted from my mobile device
RenB
Joined: 13 Jul 2022
Last visit: 30 Apr 2026
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Location: India
Concentration: Finance, Nonprofit
Schools: Stanford '26 Wharton '26 (D) Booth '26 (D) Yale '26 (D) CBS '26 (A$$$) Darden '26 (WL) HBS '26 (D) Ross '26 (A$$$$) LBS '26 (D) Tuck '26 (A$$) Kellogg '26 (A)
GMAT Focus 1: 715 Q90 V84 DI82 
GPA: 3.74
WE:Corporate Finance (Consulting)
Schools: Stanford '26 Wharton '26 (D) Booth '26 (D) Yale '26 (D) CBS '26 (A$$$) Darden '26 (WL) HBS '26 (D) Ross '26 (A$$$$) LBS '26 (D) Tuck '26 (A$$) Kellogg '26 (A)
GMAT Focus 1: 715 Q90 V84 DI82
Posts: 388
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29 May 2023, 18:18
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Arick
Hi,
Can you please provide the explanation provided by the source?
Want to know the efficient way to solve this under 2 mins
TIA
29 May 2023, 19:21
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Given: Deepti has 49 stamps which are of one-rupee. 50 paise and 25 paise denominations. The total value of her stamps is 23.50.
Asked: If the number of 25 paise stamps is greater than the number of 50 paise stamps and one-rupee stamps together, and the number of one-rupee stamps is less than 50 paise stamps, how many more 25 paise stamps than one-rupee stamps does Deepti have?
Let one-rupee, 50 paise and 25 paisa stamps be x, y & z respectively
1. x + y + z = 49
2. x + .5y + .25z = 23.5
3. z > x+y
4. x < y
z - x = ?
1) - 2)
.5y + .75z = 25.5
2y + 3z = 102
z = (102-2y)/3
(y,z) = {(0,34),(3,32),(6,30),(9,28),(12,26),(15,24),(18,22),(21,20),(24,18),(27,16),(30,14),(33,12),(36,10),(39,8),(42,6),(45,4),(48,2),(51,0)}
Since z > x+y; z > y > x
(y,z) = {(0,34),(3,32),(6,30),(9,28),(12,26),(15,24),(18,22)}
Since x = 49 - y - z < y
49 - z < 2y
y > (49-z)/2
(y,z) = {(12,26),(15,24),(18,22)}
Since z> x+y = 49-y-z + y = 49 - z
2z > 49
z > 49/2 = 24.5
(y,z) = (12,26)
x = 49 - y - z = 49 - 12 -26 = 49 - 38 = 11
x = 11; y = 12; z = 26
z - x = 26 - 11 = 15
IMO A
Asked: If the number of 25 paise stamps is greater than the number of 50 paise stamps and one-rupee stamps together, and the number of one-rupee stamps is less than 50 paise stamps, how many more 25 paise stamps than one-rupee stamps does Deepti have?
Let one-rupee, 50 paise and 25 paisa stamps be x, y & z respectively
1. x + y + z = 49
2. x + .5y + .25z = 23.5
3. z > x+y
4. x < y
z - x = ?
1) - 2)
.5y + .75z = 25.5
2y + 3z = 102
z = (102-2y)/3
(y,z) = {(0,34),(3,32),(6,30),(9,28),(12,26),(15,24),(18,22),(21,20),(24,18),(27,16),(30,14),(33,12),(36,10),(39,8),(42,6),(45,4),(48,2),(51,0)}
Since z > x+y; z > y > x
(y,z) = {(0,34),(3,32),(6,30),(9,28),(12,26),(15,24),(18,22)}
Since x = 49 - y - z < y
49 - z < 2y
y > (49-z)/2
(y,z) = {(12,26),(15,24),(18,22)}
Since z> x+y = 49-y-z + y = 49 - z
2z > 49
z > 49/2 = 24.5
(y,z) = (12,26)
x = 49 - y - z = 49 - 12 -26 = 49 - 38 = 11
x = 11; y = 12; z = 26
z - x = 26 - 11 = 15
IMO A
