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01 Apr 2025, 00:30
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
44% (02:43) correct
56%
(03:05)
wrong
based on 107
sessions
History
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Time
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Not Attempted Yet
Rob’s latest meal contained 660 calories, derived from either protein or fat. Rob consumed x grams of protein, at y calories per gram and (120 – x) grams of fat, at (y + 5) calories per gram. Did Rob consume more protein or more fat?
(1) If Rob had consumed 10 more grams of protein and 20 more grams of fat, his meal would have contained 880 calories.
(2) If Rob had consumed (120 – x) grams of protein and x grams of fat, his meal would have contained greater than 660 calories.
(1) If Rob had consumed 10 more grams of protein and 20 more grams of fat, his meal would have contained 880 calories.
(2) If Rob had consumed (120 – x) grams of protein and x grams of fat, his meal would have contained greater than 660 calories.
01 Apr 2025, 06:00
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Bunuel
Given, Calories = y*x + (120-x)*(y+5) = 660
Question: Is x > 120-x?
Question: Is x > 60?
Statement 1: 10y + 20*(y+5) = 880-660 = 220
i.e. y = 50 which also gives the exact value of x while substituted in the equation obtained for calories hence
SUFFICIENT
Statement 2: (120 – x)*y+x*(y+5) > 660
which is possible only if the quantity of fat now is increasing because it has more calories
i.e. x > 120-x
i.e. x > 60
SUFFICIENT
Answer: Option D
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01 Apr 2025, 22:49
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Bunuel
Interesting DS question.
Given :
Consumption of protein = x gm
Consumption of fat = 120-x gm
calories per gm
protein = y per gm
fat = (y+5) per gm
total calories = 660
we need to find : Is x > 120-x ?
660 = xy + (120-x) (y+5)
solving we get,
60 = 120 y - 5x
12 = 24 y -x ———————————> equation 1
STATEMENT 1:
(1) If Rob had consumed 10 more grams of protein and 20 more grams of fat, his meal would have contained 880 calories.
880 = (x+10)* y + (140 -x ) * (y+5)
180 = 150 y -5x
36 = 30 y - x —————— > equation 2
Subracting eqn 1 and eqn 2, we get
6y =24
y= 4 and x = 84
x = 84, 120-x < 84. Hence, STATEMENT 1 is SUFFICIENT
STATEMENT 2:
(2) If Rob had consumed (120 – x) grams of protein and x grams of fat, his meal would have contained greater than 660 calories.
(120-x)*y + x *(y+5) > 660
120y + 5x > 660
24y + x > 132 ——————-> equation 3
adding eqn 1 and ean 3, we get
48 y > 144
y > 3
if y > 3, substitute in equation 3, we get x > 60
if X > 60, then 120-x < 60
Hence STATEMENT 2 is SUFFICIENT.
Both, the statements are individually sufficient to answer. OPTION D
