The main purpose of this research was to investigate empirically the Wechsler Intelligence Scale for Children -- the third Jordanian version (hereinafter WISC-III-Jordan) profiles to analyze cognitive factors for 'twice-exceptional' (2E) children characterizing 'mathematical giftedness with learning disabilities (MG/LDs). The paper examined whether WISC-III-Jordan, the latest adapted version in Jordan, is a useful psychometric assessment tool for providing a partial picture of the cognitive weaknesses and strengths of 2E learners. Thirty MG/LDs students (16 girls and 14 boys) and a control group of 22 'intellectually average students with learning disabilities' (Average-IQ/LDs) (10 girls and 12 boys) were administered the WISC-III-Jordan. The two experimental and control groups, aged between 11 and 12 years, were chosen from three public primary schools in Amman, Jordan. While differences between the two groups were investigated, a comparison of 17 factors was made using five cognitive classification systems: Wechsler (1974 and 1991), Horn (1989), Bannatyne (1974), Kaufman (1975, 1994), and Rapaport et al., (1945-1946), in addition to the ACID profile (Arithmetic, Coding, Information, and Digit Span). The findings revealed that the MG/LDs sample demonstrated a significant discrepancy between the verbal and performance IQ subscales, but no significant scattered subtest profile was yielded. Relative strengths were shown in four subtests: Comprehension, Arithmetic, Vocabulary, and Picture Completion. Both experimental and control groups showed relative weaknesses in three subtests: Coding, Information, and Similarities. The analysis of the cognitive systems revealed that the Rapaport et al. (1945-1946) and Kaufman (1994) models were the most powerful for discriminating between the two groups. As opposed to the ACID profile, the Bannatyne (1974) model was the only classification not found to be useful in diagnosing students with learning disabilities. Finally, while the MG/LDs group showed significant relative strength in the visual-perceptual awareness and coordination compared to the Average-IQ/LDs group, both groups showed relative weaknesses in Sequencing Ability, Visual-Motor Coordination, and Broad Speediness.